1. Given the equations: $$\sqrt{a} + \sqrt{b} = 5$$ $$\sqrt{a} - \sqrt{b} = 1$$ 2. Add the two equations to eliminate $\sqrt{b}$: $$ (\sqrt{a} + \sqrt{b}) + (\sqrt{a} - \sqrt{b}) = 5 + 1 $$ $$ 2\sqrt{a} = 6 $$ $$ \sqrt{a} = 3 $$ 3. Square both sides to find $a$: $$ a = 3^2 = 9 $$ 4. Substitute $\sqrt{a} = 3$ into the first equation: $$ 3 + \sqrt{b} = 5 $$ $$ \sqrt{b} = 5 - 3 = 2 $$ 5. Square both sides to find $b$: $$ b = 2^2 = 4 $$ 6. Therefore, the values are: $$ a = 9, \quad b = 4 $$