1. **Problem statement:** Calculate the expansion of the expression $ (2x+3)^5 $. 2. **Formula used:** We use the Binomial Theorem, which states: $$ (a+b)^n = \sum_{k=0}^n \binom{n}{k} a^{n-k} b^k $$ where $\binom{n}{k}$ is the binomial coefficient. 3. **Apply the formula:** Here, $a=2x$, $b=3$, and $n=5$. 4. **Calculate each term:** $$ \binom{5}{0}(2x)^5 3^0 = 1 \cdot (2x)^5 \cdot 1 = 32x^5 $$ $$ \binom{5}{1}(2x)^4 3^1 = 5 \cdot 16x^4 \cdot 3 = 240x^4 $$ $$ \binom{5}{2}(2x)^3 3^2 = 10 \cdot 8x^3 \cdot 9 = 720x^3 $$ $$ \binom{5}{3}(2x)^2 3^3 = 10 \cdot 4x^2 \cdot 27 = 1080x^2 $$ $$ \binom{5}{4}(2x)^1 3^4 = 5 \cdot 2x \cdot 81 = 810x $$ $$ \binom{5}{5}(2x)^0 3^5 = 1 \cdot 1 \cdot 243 = 243 $$ 5. **Combine all terms:** $$ (2x+3)^5 = 32x^5 + 240x^4 + 720x^3 + 1080x^2 + 810x + 243 $$ This is the fully expanded form of $ (2x+3)^5 $.