This study consists of two parts. In the dose-escalation part, ASP5878 (orally available novel small-molecule FGFR 1,2,3 and 4 inhibitor, multiple dosing once-a-day (q.d.), multiple dosing twice-a-day (b.i.d.) or 5-day on/2-day off dosing twice-a-day (5on-2off)) is administered to participants with solid tumors in an increasing dose manner, and the tolerability, safety, pharmacokinetics (PK), pharmacodynamics (PD) and efficacy of ASP5878 are evaluated in these participants. Cycle 0 consists of 3 days and Cycle 1 and subsequent cycles consist of 28 days each in the dose-escalation part. In the expansion part, 16mg twice-a-day 5-day on/2-day off dose of ASP5878 (5on-2off) is administered to participants with solid tumors and safety, PK, PD and efficacy of ASP5878 are evaluated. The expansion part starts from Cycle 1 and each cycle consists of 28 days.