$5^{1/2} \times 5^{1/2} = ?$

By the product rule the exponents add: $\tfrac{1}{2} + \tfrac{1}{2} = 1$, so $5^{1/2}\times 5^{1/2} = 5^1 = 5$ (equivalently $\sqrt{5}\cdot\sqrt{5}=5$).