First multiply each term by 24(the common denominator found by 8×3) to remove the fractions and make things easier.
[tex]24(5) + 24( \frac{x - 2}{3} ) = 24( \frac{x + 3}{8} )[/tex]
This will give you,
[tex]120 + 8(x - 2) = 3(x + 3)[/tex]
Then just continue to simplify and isolate the variable.
[tex]120 + 8x - 16 = 3x + 9[/tex]
[tex]8x + 104 = 3x + 9[/tex]
[tex]5x = - 95[/tex]
[tex]x = - 19[/tex]
