Answer
$a = 0.86~m/s^2$
Work Step by Step
$ma = F_T ~sin(\theta)$
$mg = F_T ~cos(\theta)$
Let's divide the first equation by the second equation:
$\frac{a}{g} = tan(\theta)$
$a = g ~tan(\theta) = (9.80 ~m/s^2)\cdot ~tan(5.0^{\circ})$
$a = 0.86~m/s^2$
The acceleration is $a = 0.86~m/s^2$