We live in a rent home and the sewer backed up on Sunday and I called the landlord twice with no response so we stayed the night with my in-laws, I called the landlord twice Monday with no response and had to stay the night with the in-laws again. Today is Tuesday and I called the landlord again with no answer so I called a plumber. We have only lived in the house for 5 days when this mess started, do we have the right to have her reimburse us for the plumber and deduct the two nights from our rent?

You need to send a certified letter telling him you are going to the magistrate over this if he doesn't resolve it. In the meantime, ask neighbors if they have the same problem and call the water department it could be their sewer system backing up.

It will depend on first what was the cause of the back up ? If something was flushed down by you, then normally now, So a report from the plumbing explaining what caused the blockage will be helpful

Also was things like this covered in the lease agreement ?

But I do not see deduction from rent, not calling a plumber for 2 days was your choice, also many people have to live in home for one day or so, waiting on plumbing to be repaird

Not calling a plumber was not our choice when the landlord is responsible. The plumber pulled two dryer sheets out and we haven't even done laundry in the home. There is no rental/lease agreement and she specifically stated that repairs are her responsibility. If we had a working toilet we could have stayed in the home but four people with one bathroom and unable to use the toilet was not feasible to stay in the home.

Many towns also require the towns building inspector to do an inspection prior to any tenants moving in. You might want to look into that