download data from turbotax 2023 that reached limit of 5 and import into new copy of turbotax 2023

Are you using the Desktop installed program?  The returns are only on your computer.  You need to copy the data file ending in .tax2023 to the other computer to open in the program.  It should be in your Documents in a Turbo Tax folder.  

Did you install it on the same computer?  Here's how to activate a different version. There is a way to have 2 licenses. You don't need to install the second version just enter the License Code. Under Help - Switch Product - Activate new product. Don't know what that will do or what benefit you will get.

Don't think it will allow you to efile more than 5. 5 is an IRS limit.  

If you try to open the return in another program or computer you may have trouble.  After you get the program installed or reinstalled the first thing to do before you open your tax return is to update the program and install any state programs you had. Then open your file. So you first might need to start a fake return to be able to download the state program (go to FILE - NEW). Enter some basic information, then go to the state tab and download the state program. Then try to open your existing return, go to FILE - OPEN

Or if you are using the Online version and want to switch to the Desktop program you need to download the .tax2023 file from online.

Save the tax file
https://ttlc.intuit.com/community/saving/help/how-do-i-save-my-turbotax-online-return-as-a-tax-data-file/00/25740

The limit of 5 e-files is set by the IRS, not by TurboTax. It applies to the user (the person), not to a particular copy of the software. Installing a new copy of TurboTax will not allow you to e-file more than 5 federal tax returns. All do-it-yourself tax software products are subject to the same IRS limit.