Find the domain of the vector function $\displaystyle \vec{{r}}{\left({t}\right)}=<{t}^{{2}},\sqrt{{{t}+{2}}},\sqrt{{{5}-{t}}}>$

Domain: $\displaystyle {\left\lbrace{t}{\mid}\right.}$ $\displaystyle \le{t}\le$ $\displaystyle {\rbrace}$