Inclusion Criteria:

          -  A diagnosis of: Arm A: AML according to the World Health Organization (WHO) 2016
             criteria with relapsed or refractory disease and have exhausted, or are ineligible for
             therapeutic options, or high-risk or very high-risk MDS according to revised
             International Prognostic Scoring System (IPSS-R) and relapsed or refractory disease
             after at least 1 course of hypomethylating therapy or induction therapy; Arm B: newly
             diagnosed AML or relapsed or refractory AML (2016 WHO classification) (bone marrow)
             unsuitable for intensive treatment (including stem cell transplantation) with a
             curative intent, but eligible to receive AZA treatment or high-risk or very high-risk
             MDS according to IPSS-R unsuitable for intensive treatment (including stem cell
             transplantation) with a curative intent, but eligible to receive AZA treatment

          -  Eastern Cooperative Oncology Group (ECOG) performance status grade of 0 or 1

          -  Women of childbearing potential must have a negative highly sensitive serum
             (beta-human chorionic gonadotropin) at screening and again within 48 hours prior to
             the first dose of study treatment. A urine or serum test is acceptable at subsequent
             time points

          -  A woman of childbearing potential must agree to all the following during the study and
             for 30 days after the last dose of study treatment: a) use a barrier method of
             contraception; b) use a highly effective preferably user-independent method of
             contraception; c) not to donate eggs (ova, oocytes) or freeze for future use for the
             purposes of assisted reproduction; d) not plan to become pregnant; e) not breast-feed

          -  A male must agree to all the following during the study and for 90 days after the last
             dose of study treatment: a) wear a condom when engaging in any activity that allows
             for passage of ejaculate to another person; b) not to donate sperm or freeze for
             future use for the purpose of reproduction; c) not plan to father a child. In
             addition, the participant should be advised of the benefit for a female partner to use
             a highly effective method of contraception as condom may break or leak

        Exclusion Criteria:

          -  Acute promyelocytic leukemia according to World Health Organization 2016 criteria

          -  Known central nervous system involvement

          -  Prior treatment with a dihydroorotate dehydrogenase (DHODH) inhibitor for an oncology
             indication or intolerance to a DHODH inhibitor given for non-oncology indication

          -  Toxicities (except for alopecia, peripheral neuropathy, thrombocytopenia, neutropenia,
             anemia) from previous anticancer therapies that have not resolved to baseline or to
             Grade 1 or less

          -  Known allergies, hypersensitivity, or intolerance to JNJ-74856665 or AZA or the
             excipients of these treatments