You want to hold back five days of rent? That hardly seems worth it.
I'm not in a position to review the leases in order to tell you if you have a plausible argument that the new lease agreement is a wholly independent agreement, or if it represents a continuation of the prior lease; but given that failure to pay rent on time can get you hit with a notice of eviction and a possible eviction lawsuit, with all that entails for your credit and future ability to rent, I personally would simply pay the rent even if I thought I had basis to pay the last five days of rent at the end of the month.

