1. **State the problem:** We need to find an angle whose complement is 5 times as large as the angle itself. 2. **Recall the definition of complementary angles:** Two angles are complementary if their sum is $90^\circ$. 3. **Set up variables:** Let the angle be $x$ degrees. Then its complement is $90 - x$ degrees. 4. **Write the equation based on the problem statement:** The complement is 5 times the angle, so $$90 - x = 5x$$ 5. **Solve the equation:** $$90 - x = 5x$$ $$90 = 5x + x$$ $$90 = 6x$$ $$x = \frac{90}{6}$$ $$x = 15$$ 6. **Find the complement:** $$90 - x = 90 - 15 = 75$$ 7. **Answer:** The angle is $15^\circ$ and its complement is $75^\circ$.