\( \frac{2}{5} m - 7 \leq 17 \)

To solve the inequality \( \frac{2}{5} m - 7 \leq 17 \), follow these steps:

1. Add 7 to both sides of the inequality:
\[
\frac{2}{5} m - 7 + 7 \leq 17 + 7
\]
This simplifies to:
\[
\frac{2}{5} m \leq 24
\]

2. Next, multiply both sides by \( \frac{5}{2} \) to isolate \( m \). Since \( \frac{5}{2} \) is positive, the inequality direction remains the same:
\[
m \leq 24 \times \frac{5}{2}
\]

3. Calculate the right-hand side:
\[
24 \times \frac{5}{2} = 24 \times 2.5 = 60
\]

Thus, the solution to the inequality is:
\[
m \leq 60
\]