The mortgage company at my bank that originates brokered and wholesale loans and sells the loans in the secondary market.

Considering that they use more than 5 providers, are they required to provide the use provider disclosure (Good Faith Estimate)and a list (if they use more than 5)?

You don't have to give the customer the list.

What about use provider disclosure (Good Faith Estimate)? Do they have to give it (considering use of more than 5 providers)?

Yes:

3500.7(e) (4) If the lender maintains a controlled list of required providers (five or more for each discrete service) or relies on a list maintained by others, and at the time of application the lender has not yet decided which provider will be selected from that list, then the lender may satisfy the requirements of this section if the lender:
(i) Provides the borrower with a written statement that the lender will require a particular provider from a lender-controlled or -approved list; and
(ii) Provides the borrower in the Good Faith Estimate the range of costs for the required provider(s), and provides the name of the specific provider and the actual cost on the HUD-1 or HUD-1A.