Fifth Powers of Sine and Cosine

If $\theta$ is an acute angle and $\cos2\theta = \frac{3}{5}$, determine the value of $\sin^5 \theta + \cos^5\theta$. The answer is in the form $\frac{a\sqrt{b}}{c}$ where $a,b,c$ are integers, $\gcd(a,c) = 1$ and $b$ is square-free. Input the answer as $a+b+c$.