1. **State the problem:** We need to find an angle whose complement is 5 times as large as the angle itself. 2. **Define variables:** Let $x$ be the measure of the angle in degrees. 3. **Recall the complement rule:** The complement of an angle $x$ is $90 - x$ degrees. 4. **Set up the equation:** According to the problem, the complement equals 5 times the angle: $$90 - x = 5x$$ 5. **Solve the equation:** Add $x$ to both sides: $$90 = 5x + x$$ $$90 = 6x$$ Divide both sides by 6: $$90 = \cancel{6}x \Rightarrow \frac{90}{\cancel{6}} = x \Rightarrow 15 = x$$ 6. **Interpret the result:** The angle measures $15$ degrees. 7. **Check:** The complement is $90 - 15 = 75$ degrees, which is indeed 5 times $15$. **Final answer:** The angle is $15$ degrees.