Answer
$\frac{1}{16}$.
Work Step by Step
$2+\sqrt{t}=\sqrt{t+5}$
Squaring both sides:
$\begin{align}
& 2+\sqrt{t}=\sqrt{t+5} \\
& {{\left( 2+\sqrt{t} \right)}^{2}}={{\left( \sqrt{t+5} \right)}^{2}} \\
& {{2}^{2}}+2\times 2\times \sqrt{t}+t=t+5 \\
& 4+4\sqrt{t}+t=t+5
\end{align}$
Subtract $\left( t \right)$ on both sides.
$\begin{align}
& 4+4\sqrt{t}+t-t=t+5-t \\
& 4+4\sqrt{t}=5
\end{align}$
Subtract $4$ on both sides,
$\begin{align}
& 4+4\sqrt{t}=5 \\
& 4+4\sqrt{t}-4=5-4 \\
& 4\sqrt{t}=1
\end{align}$
Divide by $4$ on both sides,
$\begin{align}
& 4\sqrt{t}=1 \\
& \frac{4\sqrt{t}}{4}=\frac{1}{4} \\
& \sqrt{t}=\frac{1}{4}
\end{align}$
Square both sides:
$\begin{align}
& {{\left( \sqrt{t} \right)}^{2}}={{\left( \frac{1}{4} \right)}^{2}} \\
& t=\frac{1}{16}
\end{align}$
Thus, the required value is $t=\frac{1}{16}$.
