How to save x5d sounds in laptop

https://www.manualslib.com/manual/889655/Korg-X5d.html
https://www.manualslib.com/manual/1002683/Korg-X5d.html

Hold PROG and +10 while turning it on.

That should initialize the unit to factory fresh.

That sounds like a manufacture date being flashed. Have you checked the battery? If you can't backup first, all your changes (custom sounds) will be lost, but that might be what you are looking at. Replace the battery, or have a service center do so. You'll want to reset after.

Try ROM check first.

Initialization: Hold Page + and Page - while turning it on.
Preload: Global Screen 5A, then select "OK".
ROM Check: Hold Edit and Global/Multi while turning it on.

Guide:
How to Initialize reset and preload on the Korg X5 X5D DR SweetCare

Korg X5DR X5D Soundbanks

Just go to COMBI mode.



Press PAGE+. The display may look like this :
or

In the example above, A03 and A49 is a sound PROGRAM number.
OFF and OFF is a Layer 3 and 4, were not activated.
So in our example, we only activate two voices (two layers).
X5D can combine up to 8 voice. To view the Layer 5-8, press PAGE +.
To change the sound of your choice, move the cursor to the corresponding layer, use this button:


then change the value with the slider / value key (YES and NO):

You can also set the level of each layer.
Press PAGE + until a menu appears LEVEL.
Move the cursor and sets its value

Did you try to get to Global mode, and then check if the tune is 440 hz?
Check the Global Settings. The tuning might either be altered or the key transposed..

Press:
1- GLOBAL
2- PAGE+ or PAGE- ,untill the display show "TRANSPOSE".
Set the value to "0" using YES / NO or VALUE slider.

Check the output socket for corrosion, this would stop the sound from getting to the amp. Plug in an output cable and wiggle it around to see if it works intermittently. Plug it in and out a few times and see. We are looking for a dirty connection.

There's a watch type battery (flat disc) on one of the boards inside the X5D. This maintains the settings while the keyboard is switched off and could be the whole problem.
The keys are on two different circuit boards connected with a multi-pin cable. If the cable were dislodged I would expect it to simply cut off half the keys but it's probably worth checking.

You can't always believe the display in regard to the model... Try finding the revision level display that will tell you what you have... It is NOT likely a seller would strip a X5D case to try to fool you.
Find what the difference is in the model and test your unit for that feature.