The land lord wants to terminate my lease as his house he is living in now was foreclosed on.
And wants to live in my rental.I need to know how a buy out works and what I can ask for as I have 5 months left and have been in this house for 4 and half yrs with no problems. Is there laws in Florida for this?

I don't believe a landlord can terminate a lease early, even if they are moving back in, but they can not renew the lease.

A buyout is simply an agreement between you and the landlord to terminate the lease early in exchange for some consideration. Generally 2 months rent is considered customary.