It's raining fives

$\left(\color{#20A900}{\square}5\right)^2 = \color{#3D99F6}{\square}25$

Each square above represents a positive integer. Let $m$ and $n$ denote the values that fill in the green and blue squares, respectively, satisfying the equation. Then what is the relationship between $m$ and $n?$

Details and Assumptions:

• This is an arithmetic puzzle, where $1 \square$ would represent the 2-digit number 19 if $\square = 9$. It does not represent the algebraic expression $1 \times \square$.