This number is a composite.
125 = 53 (a prime cube). It is the smallest number which is both a sum of distinct prime squares and a prime cube. [Kulsha]
Conjecture by Zhi-Wei Sun to be the largest power (53) for which there is no prime between it and the previous power (112). The other prime gaps between powers are in (23, 32), (25, 62) and (52, 33). [Caldwell]