It isn't a problem to transfer from Savings to Checking. It is SOP. Just provide your savings statement and the bank statement showing the transfer.
I didn't realize it was cash money. I thought it was funds already in savings that was transferred. Depending upon when the cash was deposited into the savings and then subsequently transferred it could be disallowed. That's the whole reason they ask for the bank statements is to see the timeline.
Yes, Firemediii - the $5k will most likely be disallowed if the cash was deposited into savings and not seasoned for 60+ days. This is something that the OP's LO will know.
OP, talk with your LO. It is best to open up with them right away so you can take steps to do what you need to do if the funds are not counted in your closing funds. Or if they are, then you don't have to fret about it. Most good LO's really know what the u/w will accept or not. They want you to close. Remember, the LO is on your side.