Code 5 makes no sense. Code 5 is for a prohibited transaction which is almost impossible to have with an HSA. Prohibited transactions are such things as you selling investments to or buying investments from the HSA or using the HSA as collateral for a loan. If the distribution really was the result of a prohibited transaction, the funds are permanently taxably distributed not not permitted to be moved to another HSA.
If the HSA was distributed to you and you deposited the money into anther HSA, the distribution should be reported on Form 1099-SA with code 1. If the HSA was moved by trustee-to-trustee transfer where the funds were never paid to you, there should have been no Form 1099-SA at all.
Contact the payer to issue a corrected code-5 Form 1099-SA showing $0 distributed and to either issue a code-1 Form 1099-SA in its place or no other Form 1099-SA at all depending on how the funds were moved.
Agreed ... code 5 is absolutely wrong ... it should be either a code 1 (if you got the check and made the deposit to the other HSA yourself) OR no form should have been issued for a direct trustee to trustee rollover.
In the program, simply use code 1 so you can file the return while they issue you a corrected form ... this is the screen you should see to indicate the rollover ...
You can't just use a different code in TurboTax without risking a challenge from the IRS. The payer has sent a copy of the Form 1099-SA to the IRS and the code 5 on this form is telling the IRS that this distribution was not eligible for rollover, is subject to income tax and, if you are under age 65, to a 20% additional tax.