#### Answer

x = -15

#### Work Step by Step

$\frac{x}{5} - 7 = \frac{x}{3} - 5$
Subtract $\frac{x}{3}$ from both sides:
$\frac{x}{5} - \frac{x}{3} - 7 = -5$
$\frac{3x}{15} - \frac{5x}{15} - 7 = -5$
$\frac{-2x}{15} - 7 = -5$
Add 7 to both sides:
$\frac{-2x}{15} = 2$
Multiply both sides by the reciprocal, $-\frac{15}{2}$:
$-\frac{15}{2}(\frac{-2x}{15}) = 2(-\frac{15}{2}$)
x = -15