Question 161995
Let n be the smaller number.
Then the larger number is {{{n+5}}}

You are given
{{{n^2 + (n+5)^2 = 5n^2}}}
{{{n^2 + n^2 + 10n + 25 = 5n^2}}}
{{{0 = 3n^2 - 10n - 25 }}}
{{{0 = (3n + 5)(n-5)}}}
So either {{{3n+5=0}}}  or {{{n-5=0}}}
so n is either {{{-5/3}}} or {{{5}}}

Check value for n works. 5 does. does -5/3?