Can a landlord and a co-tenant enter into a mutual agreement to terminate the lease for one tenant without the consent of all tenants?

There is one lease with 5 names (tenants). ALL 5 names AND the landlord have to agree to end the lease.

In regards to the lost rent from the 5th tenant. The other 4 need to make up the difference and pay the rent in FULL each month. Then the other 4 can sue the 5th for back rent. The landlord is NOT involved in this.

No. You're responsible for your portion of the lease, and if you don't contribute, I'm guessing the other tenants could bring legal action against you. All five should be responsible until the end of the contract.

Nope. Any change to a lease is only valid if agreed upon by ALL parties on the original. The leaving tenant is still bound to the original lease.

Has or is the contract coming to an end? If so then one person has decided not to re sign and they can do that, same goes for raises in rent, it can only be done at the beginning of a new contract, not in the middle of one.

If it is in the middle of the contract and each person doesn't have their own contract with the landlord, so the 5 people have one contract with the landlord then all have to agree to any change

If you are in the US, the only way a lease can be altered is if all parties agree. What that means is thatif one person on the lease does not agree to terminate it, the lease cannot be terminated.

What did you agree too? For the remainder of the lease he can't increase your rent if he does it makes the lease worthless and no point you signing it in the first place

No. ALL parties to a lease contract must agree. The old contract voided and a new one drawn up.

Peace.

no, for the duration of the signed lease by all parties, nothing can be changed