(a) Use the reduction formula $$\int {\sin^n(x)}\, dx = -\frac{1}{n}\cos(x)\sin^{n-1}(x)+\frac{n-1}{n}\int {\sin^{n-2}(x)}\, dx$$ and the formula $$\int_{0}^{\,\pi/2} {\sin^n(x)}\, dx = \frac{n-1}{n}\int_{0}^{\,\pi/2} {\sin^{n-2}(x)}\, dx$$ to evaluate the integral $$\int_{0}^{\,\pi/2} {\sin^3(x)}\, dx.$$

(b) Use the above formulas in part(a) to evaluate the integral $$\int_{0}^{\,\pi/2} {\sin^5(x)}\, dx.$$