Question 769226
Side length original square, s.
Original area, {{{s^2}}}.


If sides become s-5 and s+3, then {{{s^2-(s-5)(s+3)=7}}}
If sides become s+3 and s+2, then {{{(s+3)(s+2)-s^2=62}}}
Find s.


The "7" equation:
{{{s^2- ( s^2-5s+3s-15)=7}}}
{{{s^2-(s^2-2s-15)=7}}}
{{{s^2-s^2+2s+15=7}}}
{{{2s=7-15=-8}}}
{{{s=-4}}} which is nonsense.


The "62" equation:
{{{s^2+5s+6-s^2=62}}}
{{{5s+6=62}}}
{{{5s=62-6}}}
{{{5s=56}}}
{{{highlight(s=56/5=11&1/5)}}}


Something is wrong in your description.  The first part fails but the second part succeeds.