Yes, they are true. Examples, using the inbuilt calculator here:
$${\sqrt{{{\mathtt{5}}}^{{\mathtt{2}}}}} = {\mathtt{5}}$$
$${\sqrt{{\left(-{\mathtt{5}}\right)}^{{\mathtt{2}}}}} = {\mathtt{5}}$$
$${{\sqrt{{\mathtt{5}}}}}^{\,{\mathtt{2}}} = {\mathtt{5}}$$
$${{\sqrt{-{\mathtt{5}}}}}^{\,{\mathtt{2}}} = -{\mathtt{5}}$$
.
Yes, they are true. Examples, using the inbuilt calculator here:
$${\sqrt{{{\mathtt{5}}}^{{\mathtt{2}}}}} = {\mathtt{5}}$$
$${\sqrt{{\left(-{\mathtt{5}}\right)}^{{\mathtt{2}}}}} = {\mathtt{5}}$$
$${{\sqrt{{\mathtt{5}}}}}^{\,{\mathtt{2}}} = {\mathtt{5}}$$
$${{\sqrt{-{\mathtt{5}}}}}^{\,{\mathtt{2}}} = -{\mathtt{5}}$$
.