Simplify the product \( \frac{5}{n+1} \cdot \frac{n+1}{n+3} \) \( \begin{array}{l}\frac{5 n+1}{n^{2}+4 n+3} \\ \frac{5 n+5}{n^{2}+4 n+3} \\ \frac{5}{n+3} \\ \frac{5 n+1}{n+3}\end{array} \)

To simplify the product \( \frac{5}{n+1} \cdot \frac{n+1}{n+3} \), we can multiply the fractions directly. When we multiply \( \frac{5}{n+1} \) by \( \frac{n+1}{n+3} \), the \( n+1 \) in the numerator of the second fraction cancels with the \( n+1 \) in the denominator of the first fraction. This leaves us with: \[ \frac{5}{n+3} \] Thus, the simplified form of the expression is \( \frac{5}{n+3} \). The correct answer is \( \frac{5}{n+3} \).