Answer
$\dfrac{25}{4}
;\\\\
\left( n+\dfrac{5}{2} \right)^2$
Work Step by Step
The third term is equal to the square of half of the middle coefficient. Hence, the third term is
\begin{array}{l}
\left( \dfrac{5}{2} \right)^2
\\\\=
\dfrac{25}{4}
.\\\\\text{In factored form,}\\
n^2+5n+\dfrac{25}{4}
\\\\=
\left( n+\dfrac{5}{2} \right)^2
.\end{array}