1. **State the problem:** Solve for $f$ in the equation $$6 = 5 + \sqrt{64} + f$$. 2. **Recall the formula and rules:** The square root of a number $x$ is a value that, when multiplied by itself, gives $x$. Here, $\sqrt{64}$ means the number which squared equals 64. 3. **Calculate the square root:** $$\sqrt{64} = 8$$. 4. **Substitute back into the equation:** $$6 = 5 + 8 + f$$. 5. **Simplify the right side:** $$6 = 13 + f$$. 6. **Isolate $f$ by subtracting 13 from both sides:** $$6 - \cancel{13} = \cancel{13} + f - 13$$ $$6 - 13 = f$$ 7. **Calculate the left side:** $$f = -7$$. **Final answer:** $$f = -7$$