1. **State the problem:** Express $27^5$ as a power of 3. 2. **Recall the base relationship:** We know that $27 = 3^3$ because $3^3 = 3 \times 3 \times 3 = 27$. 3. **Rewrite the expression:** Substitute $27$ with $3^3$ in the original expression: $$27^5 = (3^3)^5$$ 4. **Use the power of a power rule:** When raising a power to another power, multiply the exponents: $$(3^3)^5 = 3^{3 \times 5}$$ 5. **Calculate the exponent:** $$3 \times 5 = 15$$ 6. **Final expression:** $$27^5 = 3^{15}$$ So, $27^5$ expressed as a power of 3 is $3^{15}$.