#### Answer

$c=25$

#### Work Step by Step

The third term of a perfect square trinomial is equal to the square of half of the coefficient of the middle term. Hence, to make the given expression, $
y^2+10y+c
$, a perfect square trinomial, then,
\begin{array}{l}
c=\left( \dfrac{10}{2} \right)^2
\\\\
c=\left( 5 \right)^2
\\\\
c=25
.\end{array}