How do you simplify 5 / (2(x-5)) + (3x) / (x-5)?

(5+6x)/(2(x-5)
Notes that the denominator in both elements of the expression contain $\left(x - 5\right)$ which is therefore a common factor. The expression can be written as
$\left(\frac{1}{x - 5}\right) \left(\frac{5}{2} + 3 x\right)$
$= \left(\frac{1}{x - 5}\right) \frac{5 + 6 x}{2}$
=(5+6x)/(2(x-5)