If yoiu believe that your insurer is violating their agreement to pay you the $5,000, as well as, more generally, their obligation under the terms of your policy (which is a contract) to compenstate you for covered losses, your recourse is to sue them for breach of contract; a lawsuit is, unfortunately, the only way to make them live up to their obligations when they seem unwiling to do so. That letter from them would be very good evidence in a lawsuit, since it shows what they agreed to do.