jmc

Because $△RST$ is a right triangle, $\sin R=\frac{ST}{RT}$. So $\sin R=\frac{2}{5}=\frac{ST}{5}$. Then $ST=2$.

We know that $\sin T=\frac{RS}{RT}$. By the Pythagorean Theorem, $RS=\sqrt{R{T}^2-S{T}^2}=\sqrt{25-4}=\sqrt{21}$. Then $\sin T=\boxed{\frac{\sqrt{21}}{5}}$.