Thanks to Marcus and ChongGo Sunim, I’ve been further educated on the second set of precepts.
The ones that I found online are intended for someone wishing to become a monk or nun, rather than someone like myself. They are also the traditional precepts of the Theravada tradition. As Marcus pointed out, if I were to take the next five precepts in the Mahayana tradition, they would be more or less as follows:
6. I vow not to talk about the faults of others.
7. I vow not to praise myself and disparage others.
8. I vow not to be covetous, but to be generous with material or spiritual aid.
9. I vow not to give way to anger, but to be harmonious.
10. I vow not to slander the three jewels.
These precepts seem very reasonable to me, actually. I still feel like I need to focus on the first five, for now, however. When I feel as though I’ve done well by them, the next five would be a good step.