1. The problem is to solve the equation $\sqrt{x + 5} = 8$ for $x$. 2. Recall the property that if $\sqrt{A} = B$, then $A = B^2$, provided $B \geq 0$. 3. Apply this property to the equation: $$\sqrt{x + 5} = 8 \implies x + 5 = 8^2$$ 4. Calculate the square: $$x + 5 = 64$$ 5. Solve for $x$ by subtracting 5 from both sides: $$x = 64 - 5$$ $$x = 59$$ 6. Check the solution by substituting back into the original equation: $$\sqrt{59 + 5} = \sqrt{64} = 8$$ which is true. Therefore, the solution is $x = 59$.