You appear to have two types of data: ordinal and binary. It doesn’t matter whether you give them 1 to 5 or a Likert scale...the responses is just picking a single answer from somewhere in that order.
A quick discussion of what to use on Likert scales (and other ordinal scales) can be found here.
Notice that you must check your assumptions before attempting a t-test because there is a fair chance this type of data will violate assumption (such as normality) of a paired t-test. A non-parametric alternative is Mann-Whitney. However, there is no free lunch. If you use a non-parametric you also lose power and it is harder to identify small differences. But it has less requirements before you use it.
