If I reset my iPhone 5 will the version go back to the original?

I'm currently on iPhone 6.1.3 but want to restore to see if I can get to an earlier version to jailbreak.

If you restore it, it'll still be 6.1.3. Restoring doesn't remove Apple's iOS software updates. But in all other respects it does reset the phone back to "like new" condition (software-wise).