Answer
5 cos t+C
Work Step by Step
$\int$-5 sin t dt = -5$\int$ sin t dt
= -5$\times$ -cos t +C = 5 cos t + C
To check, we differentiate the answer with respect to t:
$\frac{d}{dt}(5 cos t+C)$= (5$\times$ -sin t )+0= -5 sin t = integrand.
Hence the answer is correct.