Expected Number of Distinct Colors

Twenty five colored balls (5 blue, 5 red, 5 green, 5 yellow, 5 orange) are placed in a box. Ten balls are picked from the box without replacement. What is the expected number of distinct colors from the ten balls? The answer is in the form $\frac{\alpha}{\beta}$ for coprime integers $\alpha$ and $\beta$. Input the answer as the sum $\alpha +\beta$.