Question 1164690
{{{system(m=r-3,(m+7)(r+7)=3(m-5)(r-5))}}}


Substitute for m, first.
{{{(r-3+7)(r+7)=3(r-3-5)(r-5)}}}
{{{(r+4)(r+7)=3(r-8)(r-5)}}}
{{{r^2+11r+28=3(r^2-13r+40)}}}
{{{r^2+11r+28=3r^2-39r+120}}}
{{{3r^2-r^2-39r-11r+120-28=0}}}
{{{2r^2-50r+92=0}}}
{{{r^2-25r+46=0}}}
Factorable.
{{{(r-23)(r-2)=0}}}


Most likely {{{highlight(r=23)}}} and {{{highlight(m=20)}}}.