It would be difficult for anyone on AVVO to give you a complete answer since to do so would require at a minimum, review of the contract and other documents. Take everything to a construction attorney for a consultation.
You have a very well written question, but still, for a case like this there just isn't, and can't be, enough. Check Avvo for a reputable construction law attorney in your area, particularly one who works in the residential construction area or practice. There are often notices that need to be given to contractors and you didn't mention if those were given, if necessary.
A qualified attorney will really need to dig through everything that happened to be able to help you.
I agree that it is difficult to answer. There are a lot of facts that need to be known. Also the contract needs to be reviewed. If this was a home improvement contract it needed to follow certain legal requirements. You need an experienced construction counsel to evaluate.
Bring the contract to an experienced California construction lawyer to review the documents and the history. Here is a list of issues to discuss with the attorney:
California's Home Improvement Laws apply to all residential repair contracts in the State. Among other things, they must include a description of the services to be performed and materials to be used. In emergency service, this can be difficult sometimes. As a general rule, mold remediation is not emergency service unless the area is still wet.
Most agreements like the one described here will usually state the contractor will return the property to its pre-loss condition, or words to that effect. Contractors argue this constitutes an authorization to remediate mold. Insurance companies generally pay at least some expenses for mold remediation, assuming the mold was the result of an accident (e.g., pipe burst) and not a pre-existing condition, construction defect or a general maintenance problem.
If a contractor proceeds with work without insurance company approval but then obtains the approval after the fact, then there is no loss to the owner. A contract that does not specify the price, scope and completion date does not comply with California's Home Improvement Laws. In some instances non-compliant contracts are voidable by the consumer, but the contractor is probably entitled to the reasonable value of services rendered. You should go to work on your insurance company to pay the $5,000, if it costs that much.
I see no facts in the description that would obligate the contractor to pay for anything beyond the mold cap. That would occur, where, for example, the the contractor caused the mold. Perhaps there are other facts that would give rise to a claim like that.
If an owner wrongfully ejects a contractor from a project, the contractor may be entitled to recover lost profits, although they very rarely ever try. Moreover, if a contractor performing residential work does not provide a notice of the statutory right to cancel within three days, the owner may cancel the contract at any time.
These comments are for general informational purposes and do not create an attorney-client relationship. Do not rely on this post as "legal advice." Consult with a licensed attorney regarding the specific facts of your case and your rights and liabilities.