How do I evaluate $f_5(1)$, where $f_5(x)=5^{-m}$, when $x=5^m\frac{a}{b}$ and $5$ doesn't divide a or b or $f_5(x)=0$, when $x=0$

Question

I would like to offer my own attempt, but I honestly don't have a clue. I'm completely baffled. Any help would be appreciated.

Full question: Using results from Book A, one can show that for each non-zero rational number $x$, there is a unique $m∈\mathbb{Z}$ such that:

$x=5^m\frac{a}{b}$, $a∈\mathbb{Z}-${$0$}, $b∈\mathbb{N}$, and 5 does not divide either of a and b. We use this fact to define a function $f_5:\mathbb{Q}\rightarrow \mathbb{R}$ by,

$f_5(x)= 5^{-m}$, if $x=5^m\frac{a}{b}$,

$f_5(x)= 0$, if $x=0$

(I don't know how to do a piecewise function on here)

Write down $f_5(1), f_5(5)$ and $f_5(5^n)$ for $n∈\mathbb{N}$

I'm not sure which particular results they are referenceing from the Book A, but I don't think they are needed for the question.

Answer 1

$f_{5}(1) = 1, 1 = 5^{0}*\frac{1}{1}$

$f_{5}(5) = \frac{1}{5}, 5 = 5^{1} * \frac{1}{1}$

$f_{5}(5^n) =\frac{1}{5^{n}}, 5^{n} =5^{n} *\frac{1}{1}$

Are there any further proofs or anything required? Otherwise question seems pretty short.