#### Answer

$a=-2$

#### Work Step by Step

To solve a linear equation, we use the properties of equality and of real numbers to isolate the variable in the equation and find the solution.
For the equation $5a-2=-12$, we must first add $2$ to each side: $$5a-2+2=-12+2$$$$5a=-10$$
Next, we divide by $5$ on each side of the equation: $$\frac{5a}{5}=\frac{-10}{5}$$$$a=-2$$