Here’s a thread covering the basic process. Ground up Restoration - TAZ3 to TAZ5
In your case you essentially have the electronics of a taz 5, and close enough to the frame of a taz 3 to use that as a direct guide. You can get the x end plates from lulzbot still, and the leadscrews and lead screw nuts can be sourced new or used. Itworks3d.com can be a good source for those. In addition to what’s swapped out in that thread you are going to want to swap out the main frame to bed frame mounts, as the old style ones can shift unexpectedly. The only tricky part to the upgrade is the relocated z axis endstop wire, which requires either remaking or extending that wire. Once you have that in, and you verify your taz is a 24v tax you can essentially just load the stock taz 5 firmware, recalibrate the e steps, and go to town. Alternativly you could upgrade to 6 spec. That requires a bit more work and additional parts.
You might take a look at the taz openbuilds x and y mods after you upgrade to 5 spec as well.