There are some possible reasons why your refund is being sent by check and not direct deposit:
The IRS can only deposit refunds electronically into a bank account that is in your own name, your spouse's name, or in a joint account.
A financial institution may reject a direct deposit at its own discretion (contact your bank).
The IRS can’t deposit more than three electronic refunds into a single financial account.
The bank account information you provided was incorrect (Make sure that you provided the correct account information)
Reasons why you might have not receive your refund within the promised 5-days
Refund was offset or differed from their estimated refund amount, bringing the refund amount below the minimum threshold or above the maximum. What is a refund offset?
Your bank wouldn't accept RTP (Real Time Payments) or Same Day ACH deposits, preventing Intuit from depositing their refund 5 days ahead of when the IRS would have deposited their refund.
The IRS didn't give Intuit 5 or more days of notice in advance. This stopped Intuit from meeting the 5 days early expectations.
If TurboTax is unable to deliver the refund 5 days early, your order will be canceled and you won't be charged the 5 Day Early fee. You will receive a follow-up email with a refund and timing update, and if any cancellation is applicable.
If you don’t receive an update email or an automatic refund (if applicable) within a few days you can contact TurboTax Customer Support by clicking the link below