Is a 5 day notice to pay or quit the same as an eviction? The landlord told the appeals court he evicted me 11 times but he agreed to payments.

The property mgr agreed to accept two payments and told me not to worry about the 5 day, I could just throw it out. But when the water main broke on the house I was renting as is, he refused to fix it, and when I called for them to come pick up the rent, they refused to pick it up,instead they filed for eviction. My boyfriend filed the motion for a stay, but only said we hadn't violated the lease instead of saying they refused the rent, so the motion was denied. I filed the appeal, which got us the time we needed to find a place and move out, and the judge refunded the rent money I had posted with the court to me, but we lost the appeal. But 5 days before the end of the month the city shut the water because of the leak and we had to go to a hotel. Now he's suing me in small claims court for more than 6 months rent, and I have had to pay the outrageous water bill, hotels, moving trucks, court fees, as well as a deposit on a new place.