Your return will stay in a pending status until the IRS begins accepting returns, which happened, January 27, 2020. The status should update in approximately 24-48 hours from today but it could be longer until the IRS clears out the January backlog. For more information on the "pending" return status, please click here.
TurboTax gives an estimated date for refunds based on the IRS 21 day turnaround time. So I would not worry about the estimated timeframe given.
mine was transmitted and accepted on Jan 27. I checked the wheres my refund on feb 2 and it shows my refund should be deposited to my bank on Feb 5
No you should not be worried. The IRS only updates your refund status information once per week on Wednesdays. If you e-filed your tax return, wait at least 72 hours from the date the IRS confirms receipt of your return before checking your refund status, and at least three weeks if you mail the return instead. Here is more information on What days the IRS Makes Direct Deposits.