My intuition is that, if you look at the confounding relationship of the 2^5-2 and cross out all the terms involving the factor that you dropped then you should have the new confounding relationships. It may or may not be the confounding structure of some 2^4-1. I don't know off the top of my head, but it wouldn't surprise me either way. You may have inadvertently ended up confounding terms that you didn't need to. There's also a chance that you can now estimate some things you couldn't in the 2^5-2.
If this is a serious experiment, I would consult a statistician. I'm far from an expert on fractional factorial designs.