T-tests assess a difference in mean outcome between two groups. In this case, I assume you intend to use your 5 level ordinal response scale as such an outcome. This means that responses will be literally coded as such with the 1 indicating a response of "not at all at risk" and 5 indicating "at very high risk". This is generally considered a valid approach for the analysis of such data.
Your study design allows you to use a special paired t-test for which software is available to compute and test for differences in pre/post responses. In a 1 sample case, without a control group, you might test whether the estimated pre/post difference is consistent with having no difference (a difference of 0). It's generally bad practice to do an intervention study without a control group. This gives rise to the Hawthorne effect.
If you have a control group, then you can use a 2 sample paired t-test to compare pre/post differences between the intervention and control groups. In a future study, it might be useful to consider adjusting for certain variables, like family history, for greater precision. This would require a regression framework.