Study of GSK3359609 With Pembrolizumab and 5-fluorouracil (5-FU)-Platinum Chemotherapy in Participants With Recurrent or Metastatic Head and Neck Squamous Cell Carcinoma

Inclusion Criteria:

* Capable of giving signed informed consent
* Male or female, age \>=18 years
* HNSCC that was diagnosed as recurrent or metastatic and considered incurable by local therapies.
* Primary tumor location of the oral cavity, oropharynx, hypopharynx or larynx.
* No prior systemic therapy administered in the recurrent or metastatic setting (with the exception of systemic therapy completed \>6 months prior if given as part of multimodal treatment for locally advanced disease and no disease progression/recurrence within 6 months of the completion of curatively intended systemic treatment).
* Measurable disease per RECIST version 1.1 guidelines
* Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) score of 0 or 1.
* Adequate organ function.
* Life expectancy of at least 12 weeks.
* Female participants: must not be pregnant, not breastfeeding, and be either not a woman of childbearing potential (WOCBP); or be a WOCBP who agrees to use a highly effective method of birth control from 30 days prior to randomization and for at least 120 days after the last dose of study treatment.
* Male participants with female partners of child-bearing potential: must agree to use a highly effective contraception while receiving study treatment and for at least 120 days after the last dose of study treatment and refrain from donating sperm during this periods.
* Provide tumor tissue from excisional or core biopsy (fine needle aspirates and bone biopsies are not acceptable) acquired within 2 years prior to randomization for PD-L1 immunohistochemistry (IHC) testing by central laboratory.
* Have PD-L1 IHC CPS status by central laboratory testing.
* Have results from testing of human papilloma virus (HPV) status for oropharyngeal cancer.

Exclusion Criteria:

* Prior therapy with an anti-PD-1/L1/L2, anti-Inducible T Cell Co-Stimulatory Receptor (ICOS) directed agent.
* Systemic approved or investigational anticancer therapy within 30 days or 5 half lives of the drug, whichever is shorter. At least 14 days must have elapsed between the last dose of prior anticancer agent and the date of randomization. - Has high risk of bleeding (examples include but not limited to tumors encasing or infiltrating a major vessel \[i.e. carotid, jugular, bronchial artery\] and/or exhibits other high-risk features such as an arteriovenous fistula)
* Active tumor bleeding - Grade 3 or Grade 4 hypercalcemia.
* Major surgery less than or equal to (\<=) 28 days prior to randomization.
* Participants must have also fully recovered from any surgery (major or minor) and/or its complications before randomization
* Toxicity from previous anticancer treatment that includes: a. Grade 3/Grade 4 toxicity considered related to prior immunotherapy and that led to treatment discontinuation and b. toxicity related to prior treatment that has not resolved to \<=Grade 1 (except alopecia, hearing loss, endocrinopathy managed with replacement therapy, and peripheral neuropathy which must be \<=Grade 2).
* Received transfusion of blood products or administration of colony stimulating factors within 14 days prior to randomization.
* Central nervous system (CNS) metastases, with the following exception: Participants with asymptomatic CNS metastases who are clinically stable and have no requirement for steroids for at least 14 days prior to randomization.
* Invasive malignancy or history of invasive malignancy other than disease under study within the last 3 years with the exception of: a. any other invasive malignancy for which the participant was definitively treated, has been disease-free for \<=3 years. b. curatively treated non-melanoma skin cancer or successfully treated in situ carcinoma and/or. c. low-risk early stage prostate cancer defined as: Stage T1c or T2a with a Gleason score \<=6 and prostatic-specific antigen less than (\<)10 nanograms per milliliter (ng/mL) either treated with definitive intent or untreated in active surveillance that has been stable for the past year prior to randomization.
* Autoimmune disease or syndrome that required systemic treatment within the past 2 years.
* Has a diagnosis of immunodeficiency or is receiving systemic steroids (\>10 milligram \[mg\] oral prednisone or equivalent) or other immunosuppressive agents within 7 days prior to randomization.
* Receipt of any live vaccine within 30 days prior randomization.
* Prior allogeneic/autologous bone marrow or solid organ transplantation.
* Has current pneumonitis or history of non-infectious pneumonitis that required steroids or other immunosuppressive agents.
* Recent history (within the past 6 months) of uncontrolled symptomatic ascites, pleural or pericardial effusions.
* Recent history (within the past 6 months) of gastrointestinal obstruction that required surgery, acute diverticulitis, inflammatory bowel disease, or intra-abdominal abscess.
* Recent history of allergen desensitization therapy within 4 weeks of randomization.
* History or evidence of cardiac abnormalities within the 6 months prior to randomization which include: a. Serious, uncontrolled cardiac arrhythmia or clinically significant electrocardiogram abnormalities including second degree (Type II) or third-degree atrioventricular block. b. Cardiomyopathy, myocardial infarction, acute coronary syndromes(including unstable angina pectoris), coronary angioplasty, stenting or bypass grafting. c. Congestive heart failure (Class II, III, or IV) as defined by the New York Heart Association functional classification system. d. Symptomatic pericarditis.
* Current unstable liver or biliary disease per investigator assessment defined by the presence of ascites, encephalopathy, coagulopathy, hypoalbuminemia, esophageal or gastric varices, persistent jaundice, or cirrhosis.
* Active infection requiring systemic therapy.
* Known human immunodeficiency virus (HIV) infection, or positive test for hepatitis B active infection (presence of hepatitis B surface antigen), or hepatitis C active infection.
* History of severe hypersensitivity to monoclonal antibodies or to the chemotherapies under investigation including any ingredient used in the formulation.
* Known history of active tuberculosis.
* Any serious (\>=Grade 3) and/or unstable pre-existing medical condition (aside from malignancy).
* Any psychiatric disorder, or other condition that could interfere with participant's safety, obtaining informed consent, or compliance to the study procedures in the opinion of the investigator.
* Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to the date of randomization.