A right triangle with legs $10$ and $8$ is similar to another right triangle with corresponding legs $x$ and $5$, respectively. What is the value of $x$? Express your answer as a decimal to the nearest hundredth.
By similarity, we know that $\frac{10}{x} = \frac{8}{5}$, so therefore $x = \frac{50}{8} = \boxed{6.25}$.