$\frac{3m + 5}{4} = \frac{5m + 1}{3}$
3(3m + 5) = 4(5m + 1)
9m + 15 = 20m + 4
9m − 20m = 4 − 15
−11m = −11
m = −11 : −11
m = 1

$\frac{5x + 3}{5} = \frac{x - 5}{8}$
5(x − 5) = 8(5x + 3)
5x − 25 = 40x + 24
5x − 40x = 24 + 25
−35x = 49
$x = -\frac{49}{35}$
$x = -\frac{7}{5}$
$x = -1\frac{2}{5}$