1. **State the problem:** Convert the mixed number $2 \frac{3}{5}$ to an improper fraction in its lowest terms. 2. **Recall the formula:** To convert a mixed number $a \frac{b}{c}$ to an improper fraction, use: $$\text{Improper fraction} = \frac{a \times c + b}{c}$$ 3. **Apply the formula:** Here, $a=2$, $b=3$, and $c=5$. $$\frac{2 \times 5 + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5}$$ 4. **Simplify the fraction:** Check if $\frac{13}{5}$ can be simplified further. Since 13 and 5 have no common factors other than 1, the fraction is already in its lowest terms. 5. **Final answer:** The improper fraction form of $2 \frac{3}{5}$ is: $$\frac{13}{5}$$