(5t^3)/(15t^5) = (5t x 3t^2)/(5t^3 x 3t^2) = 5t/5t^3 = t/t^3
It's not okay, and your answer should be simplified. (You added an extra factor of 3 in your numerator.) You could have found a better set of factors:
$\displaystyle \frac{5t^3}{15t^5} = \frac{5t^3}{5t^3 \cdot 3t^2} = \frac{1}{3t^2}$