Mathematical curiosity

The first few powers of 5 share a curious property — their digits can be rearranged to express their value:

25 = 5²
125 = 5^{1 + 2}
625 = 5^{6 – 2}
3125 = (3 + (1 × 2))⁵
15625 = 5⁶ × 1²⁵
78125 = 5⁷ × 1⁸²

It’s conjectured that all powers of 5 have this property. But no one’s proved it yet.