Question

How to find all real solutions

Answer 1

$\bf \sqrt{\sqrt{x-5}+x}=5\leftarrow \textit{squaring both sides} \\\\ \sqrt{x-5}+x=25\implies \sqrt{x-5}=25-x\leftarrow \textit{squaring both sides} \\\\ x-5=(25-x)^2\implies x-5=625-50x+x^2 \\\\ 0=x^2-51x+630\implies 0=(x-30)(x-21)$

and surely you'd know what the roots are