GSK5458514 alone or with other anti-cancer drugs for prostate cancer

Inclusion Criteria:

* Provide signed informed consent. Participants must be capable of providing informed consent, which includes compliance with the requirements and restrictions listed in the Informed consent form (ICF) and in this protocol.
* Male participants greater than equal to (\>=)18 years of age (or the legal age of consent in the jurisdiction in which the study is taking place) at the time of signing the ICF.

Male participants are eligible to participate if they agree to the following during the study intervention period and for at least 195 days, after the last dose of study intervention:

Refrain from donating sperm

PLUS either:

Be abstinent from heterosexual intercourse as their preferred and usual lifestyle (abstinent on a long-term and persistent basis) and agree to remain abstinent.

OR

Must agree to use contraception as detailed below:

Agree to use a male condom and should also be advised of the benefit for a female partner to use a highly effective method of contraception as a condom may break or leak when having sexual intercourse with a woman of childbearing potential (WOCBP) who is not currently pregnant.

* Participants with mCRPC:

  * Histologically or cytologically confirmed adenocarcinoma of the prostate
  * Metastatic disease diagnosed either by radiologic imaging (Positron emission tomography \[PET\]- Computed tomography \[CT\]) and/or regular CT and/or Magnetic resonance imaging (MRI) and/or bone scan
  * Castration-resistant status as per PCWG3 criteria
* Has prior novel anti-androgen receptor therapy failure and had treatment failure with 1-2 taxane-based chemotherapy regimens including for metastatic hormone sensitive prostate cancer.
* Has (1) at least 1 soft tissue target lesion per Prostate Cancer Working Group 3 (PCWG3)-modified Response Evaluation Criteria in Solid Tumors, version 1.1 (RECIST 1.1) OR (2) if Non-Target soft tissue disease only per PCWG3-modified RECIST 1.1, may be included if a rise in Prostate-specific antigen (PSA) on 2 successive determinations at least 1 week apart (the most recent screening measurement must have been \>= 2 nanograms per milliliter (ng/mL) with testosterone levels \<50 nanograms per deciliter (ng/dL), OR (3) bone disease defined by PCWG3 (2 or more lesions on bone scan at screening), as determined by the investigator.
* Documented disease progression on most recent systemic anti-cancer therapy defined by fulfilling at least 1 of the PCWG3 criteria
* Have serum testosterone \<50 ng/dL (\<1.7 nM). Patients must have undergone bilateral orchiectomy or be on continuous androgen-deprivation therapy with a Gonadotropin-releasing hormone (GnRH) agonist or antagonist; this therapy must have been initiated at least 4 weeks prior to randomization and treatment must be continued throughout the study.
* Eastern Cooperative Oncology Group (ECOG) performance status \<=1, with no deterioration in the 2 weeks before step-up treatment period Day 1.
* Have supplied tumor tissue from a newly obtained biopsy or archival tumor tissue for retrospective detection of Prostate-specific membrane antigen (PSMA) expression and other biomarker analysis. Tissue from a newly obtained biopsy is preferred. If a newly obtained biopsy is not feasible, archival tumor tissue preferably taken after the completion of the participant's last line of therapy prior to the first dose of study drug is acceptable.
* Participants must have adequate organ function

Exclusion criteria:

* Pathological finding consistent with small cell, neuroendocrine carcinoma of the prostate or any histology different from adenocarcinoma.
* History of central nervous system (CNS) metastases or leptomeningeal disease.
* Diagnosis of invasive malignancy or history of invasive malignancy other than the disease under study within the last 5 years, except as noted below:

  * History of an invasive malignancy for which the participant was definitively treated, and in which the participant has been disease free for at least 2 years, and which, in the opinion of the principal investigator and medical monitor, is not expected to affect the evaluation of the effects of the study intervention on the currently targeted disease under study
  * Curatively treated basal cell carcinoma of the skin, superficial bladder cancer, squamous cell carcinoma of the skin, and/or in situ breast cancer may be enrolled
* Has ongoing adverse reaction(s) from prior therapy that have not recovered to \<=Grade 1 or to the baseline status preceding prior therapy, excluding \[e.g., alopecia, hearing loss, vitiligo, endocrinopathy managed with replacement therapy, and Grade 2 neuropathy\], or that the investigator, with the agreement of the sponsor, considers to be not clinically relevant for the tolerability of study intervention in the current clinical study.
* Confirmed history or recurrent autoimmune disease that has required systemic treatments in the 2 years prior to screening. Participants with prior history of autoimmune disease must be discussed with the medical monitor. Replacement therapy is not considered a form of systemic therapy (e.g., thyroid hormone for autoimmune thyroiditis or insulin is not exclusionary).
* Has evidence of interstitial lung disease, non-infectious pneumonitis, and/or a history of interstitial lung disease, non-infectious pneumonitis that required steroid.
* Has received any anti-cancer therapy or prior systemic biologic therapy, including immunotherapy within 30 days prior to first dose of study intervention.
* Prior PSMA radionuclide therapy within 2 months prior to GSK5458514 unless participant received \<2 cycles.
* Prior PSMA-Chimeric antigen receptor T cell therapy (CAR-T) cell therapy and PSMA (T cell engager) TCE/ Bispecific T cell engagers (BiTE) or other prostate Tumor-associated antigens (TAA) specific T cell engager (TCE).
* Has any history of prior allogenic or autologous bone marrow transplant or other solid organ transplant.
* Has known sensitivity to study intervention components or excipients or other allergy that, in the opinion of the investigator or medical monitor, contraindicates participation in the study.
* History of severe neurological or psychiatric disorder, including epilepsy, dementia, or major depression deemed to interfere with study assessments.
* Has had any major surgery (such as craniotomy, thoracotomy, or laparotomy, etc.) within 4 weeks prior to first dose of study intervention.
* Serious infections within 4 weeks prior to the first dose, including but not limited to infectious complications, bacteremia, severe pneumonia treated with IV antibiotics for \>=2 weeks; active infections with therapeutic IV antibiotics within 2 weeks prior to the first dose or oral antibiotics within 1 week prior to the first dose. Participants who are receiving or have received prophylactic antibiotics (e.g., prophylaxis against urinary infections) are allowed.

Liver safety exclusion criteria:

* Has an Alanine aminotransferase (ALT) value \>2.5x upper limit of normal (ULN) or \>5x ULN if documented history of liver metastases.
* Has a total bilirubin value \>1.5x ULN.
* Has cirrhosis or current unstable liver or biliary disease per investigator assessment defined by the presence of ascites, encephalopathy, coagulopathy, hypoalbuminemia, esophageal/gastric varices, or persistent jaundice.
* Has documented presence of Hepatitis B surface antigen (HBsAg), at screening or within 3 months prior to the first dose of study intervention.
* Has a positive Hepatitis C virus (HCV) antibody test result at screening or within 3 months prior to Cycle 1 Day 1 unless the participant can meet the following criteria: NOTE: Participants with a positive HCV antibody test result due to prior resolved disease can be enrolled if a confirmatory negative HCV RNA test is obtained and the participant otherwise meets entry criteria
* Has a positive HCV ribonucleic acid (RNA) test result at screening or within 3 months prior to the first dose of study intervention. NOTE: The HCV RNA test is optional, and participants with a negative HCV antibody test are not required to undergo HCV RNA testing as well.
* Is unable to adhere to the protocol defined SoA, including requirements for the Follow-up Period of the study, study procedures, restrictions, and requirements as determined by the investigator.