Pilot reported an incorrectly set altimeter setting was responsible for an altitude deviation and the kollsman window on the altimeter was too small to read correctly.

Narrative

I was on an IFR flight plan from ZZZ to ZZZ1 and being vectored; having been assigned a climbing limit of 7;000 feet. While in the climb and climbing through 5;500 feet indicated; the Departure Controller told us to cap our climb at 5;000 feet for traffic. We informed him that we showed 5;500 feet and that we would start the descent back to 5;000 feet. He stated that would be fine but that he showed us at a lower altitude and not yet reaching 5;000 feet. The Controller asked us to reset and as I was starting the process to reset the Transponder; I noticed that our altimeter setting was wrong. I had plugged in the wrong number on the ground; I suppose. The Kollsman window is small in the TB20; and I needed new glasses (it had been only about two weeks since my last eye exam; and I picked up my new glasses today; the same day as the event). Anyway; we were ultimately assigned 7;000 feet and our indicated altitude and the Controller altitude crosschecked and we flew the rest of the flight uneventfully. I will absolutely confirm the altimeter in the future so this will not happen again. I wish there was a magnifying bubble for the Kollsman window; as there was one commercially available at one time. I've heard other TB20 pilots say the same thing.