We have two inequalities to consider:

1. \(3x - 7 \leq 0\)

2. \(x + 5 > 0\)

Solve each inequality separately to find the range of values of \(x\) that satisfy both conditions.

For the first inequality:

\(3x - 7 \leq 0\)

Add 7 to both sides:

\(3x \leq 7\)

Divide by 3 (since 3 is positive, the inequality direction doesn't change):

\(x \leq \frac{7}{3}\)

For the second inequality:

\(x + 5 > 0\)

Subtract 5 from both sides:

\(x > -5\)

Now, we want to find the range of values of \(x\) that satisfy both inequalities. This means we need to find the values of \(x\) that are less than or equal to \(\frac{7}{3}\) and greater than -5. The common range is:

\(-5 < x \leq \frac{7}{3}\)