\(x^2=x^5\Rightarrow x\in\left\{0;1\right\}\)
\(5^y+5^{y+2}=650\)
\(\Rightarrow5^y.\left(1+5^2\right)=650\)
\(\Rightarrow5^y.\left(1+25\right)=650\)
\(\Rightarrow5^y.26=650\)
\(\Rightarrow5^y=650:26\)
\(\Rightarrow5^y=25\)
\(\Rightarrow5^y=5^2\)
Vậy y=2.