Taxpayers that are required to use inventories must report on the accrual basis. , So since you are not subject to accrual under these exceptions then you are free to report on the cash basis. (Note: The $5 million or less exception you mention is an exception to the exception so it does not apply here to you as you are not subject to any of the exceptions in the first place.)
Generally C corporations must report on an accrual basis.
A Partnership With C Corporation Partners
A partnership with C corporation partners must report on an accrual basis.
Trust With Unrelated Business Taxable Income
A trust that has unrelated business income must report on an accrual basis.
Tax shelters must report on an accrual basis.
Notwithstanding the above accrual requirements, the cash method can be used if the entity is not a tax shelter and is (1) engaged in a farming or tree raising business, (2) is a qualified personal service corporation, or (3) is an entity that has met the $5 million or less gross receipts test for all prior years beginning after 1985.
The cash method may also be used by most other taxpayers whose average annual gross receipts do not exceed $1 million (See Rev Proc 2001-10) and may be used by select taxpayers whose average annual gross receipts do not exceed $10 million (See Rev. Proc. 2002-28).