Question 813745
Requires squaring TWICE.


The first squaring:
{{{x-3+2*sqrt(x-3)sqrt(x+5)+x+5=16}}}
{{{2*sqrt(x-3)sqrt(x+5)=16+3-x}}}
{{{2*sqrt(x-3)sqrt(x+5)=19-x}}}


The second squaring:
{{{4*(x-3)(x+5)=(19-x)^2}}}
.
and YOU continue from here.  This will be a quadratic equation in x which you can solve by general solution to a quadratic equation, or possibly by factoring.