1. **Problem statement:** Given $\sec A - \tan A = \frac{5}{2}$, find the value of $\sec A + \tan A$. 2. **Formula and important rule:** Use the identity: $$ (\sec A + \tan A)(\sec A - \tan A) = \sec^2 A - \tan^2 A = 1 $$ This identity comes from the Pythagorean identity $\sec^2 A - \tan^2 A = 1$. 3. **Intermediate work:** Given $\sec A - \tan A = \frac{5}{2}$, let $x = \sec A + \tan A$. Using the identity: $$ x \times \frac{5}{2} = 1 \implies x = \frac{1}{\frac{5}{2}} = \frac{2}{5} $$ 4. **Explanation:** We used the product of $\sec A + \tan A$ and $\sec A - \tan A$ which equals 1. Since one factor is $\frac{5}{2}$, the other must be its reciprocal $\frac{2}{5}$. **Final answer:** $$ \sec A + \tan A = \frac{2}{5} $$