How to calculate the bandwidth of a continuous signal?
I suppose the correct expressions you meant are:

a) $5\sin(2t)$

b) $\sin(2t) + \sin(3t)$

Bandwidth is defined as the difference between the highest and lowest frequencies of a given signal ou system.

With this in mind, signal a) has one single frequency of 2 rad/s and so its bandwidth is 2-2=0 rad/s.
Similarly, signal b) has 2 frequencies: 2 rad/s and 3 rad/s. So, bandwidth is 3-2=1 rad/s.