An exponent signifies repeated multiplication. That is
... 5² = 5·5 . . . . . 5 is a factor 2 times
... 5⁵ = 5·5·5·5·5 . . . . . 5 is a factor 5 times
When you multipy these products, you get a result that has 5 as a factor 7 times.
... 5·5 × 5·5·5·5·5 = 5·5·5·5·5·5·5
As you might expect, this repeated multiplication will be expressed as 5⁷.
_____
Your rewrite is ...
... 5²·5⁵ = 5⁷