Answer
Second Student is Correct
Work Step by Step
To simplify $x^{5}$+$x^{5}$, we add the two terms and not the exponents because to add the exponents we need to multiply the terms as they would have the same base.
$x^{5}$+$x^{5}$ = 2$x^{5}$
($x^{5}$)$\times$($x^{5}$) = $x^{5+5}$ = $x^{10}$ --> Therefore Student one is wrong because you can't add the exponents as there is an addition sign and not a multiplication sign.
