Based on the available information, there is no supported way described to synchronize a Microsoft Wireless Mouse 5000 from one combo with the receiver from another combo; each set is intended to be used as shipped.
If you have a bluetooth on your PC, you can purchase a new bluetooth mouse. But, please, first check what bluetooth version is on your PC: https://support.microsoft.com/en-us/windows/hardware/bluetooth/what-bluetooth-version-is-on-a-windows-device to make sure that new bluetooth mouse will work without problems on your PC.
Of course, you can purchase a mouse with a dongle, but you will have two dongles on your PC, occupying two USB ports.