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$y = f(x) = \frac{x}{{x + 5}}$
$f(5x) = g(y)$
$g(y) = ?$

$f(5x) = \frac{{5x}}{{5x + 5}} = \frac{x}{{x + 1}}$

Given, $y = \frac{x}{{x + 5}}$

$\therefore y.x + 5y = x$

$ \Rightarrow x = \frac{{5y}}{{1 - y}}$

Now, $f(5x) = \frac{x}{{x + 1}} = \frac{{\frac{{5y}}{{1 - y}}}}{{\frac{{5y}}{{1 - y}} + 1}}$

$ = \frac{{5y}}{{4y + 1}} = g(y)$