Inclusion Criteria  Have a diagnosis of relapsed or refractory AML or ALL for Phase I and for Phase 2 have a diagnosis of relapsed or refractory AML with MLLr or NPM1 Be > 18 years of age or 20 years if required by local regulation ECOG < 2 WBC below 30,000/μL (hydroxyurea allowed prior to initiation of the study treatment) Glomerular filtration rate (GFR) ≥ 50 ml/min, assessed by the Cockcroft-Gault formula Total bilirubin ≤1.5 the upper limit of normal (ULN) (or ≤2.0 ULN for patients with known Gilbert's syndrome) Aspartate aminotransferase (AST) ≤3.0 times ULN Alanine aminotransferase (ALT) ≤3.0 times ULN Any prior treatment-related toxicities resolved to ≤Grade 1 prior to enrollment, with the exception of ≤Grade 2 alopecia Have an estimated life expectancy ≥3 months, based on the investigator's assessment  Exclusion Criteria:  Has a left ventricular ejection fraction (LVEF) <45%, as determined by ECHO Histological diagnosis of acute promyelocytic leukemia Received systemic calcineurin inhibitors within 4 weeks prior to the first dose of DSP 5336 Has had abnormal ECGs that are clinically significant, such as QT prolongation (QTc >450 msec for males and >470 msec for females, with QTc corrected according to Fridericia's formula [QTcF]) Has an active, uncontrolled, bacterial, viral, or fungal infection requiring systemic therapy Receives concurrent sensitive substrates with a narrow safety window or strong inhibitors or inducers of CYP3A4/5, including specifically: ketoconazole, itraconazole and isavuconazole. Other antifungals that are used as standard of care to prevent or treat infections are permitted Also if a patient is on one of these excluded antifungals he/she can be taken off or switched to a permitted azole 7 or more days prior to first dose, then the patient could be allowed on study (Arm B) Received immunotherapy, including tumor vaccines and checkpoint inhibitors, within 42 days prior to the first dose of DSP-5336 Has been on other investigational treatment within the previous 4 weeks prior to the first dose of DSP-5336 Had major surgery within 28 days prior to the first dose of DSP-5336 Has active central nervous system leukemia