Answer
$2t+2\sqrt{10t}+5$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$, or the square of a binomial, and the properties of radicals, the given expression, $
(\sqrt{2t}+\sqrt{5})^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
(\sqrt{2t})^2+2(\sqrt{2t})(\sqrt{5})+(\sqrt{5})^2
\\\\=
2t+2\sqrt{10t}+5
.\end{array}