I need help troubleshooting a Mac Pro 5,1.

If you are getting a kernel panic log it and post it here:

Mac OS X: How to log a kernel panic - Apple Support

Otherwise:

Note the time of the next unintended reboot. After rebooting open the Console app in Finder>Applications>Utilities and look for log entries at the time of the reboot. Post suspicious ones here.

Look before the log entry that starts with BOOT_TIME since that is the first line of a bootup

Mac Pro with Xeon processor uses Error Correcting Code memory. Memory problems do not fester undetected in these Macs. Correctable errors are corrected on-the-fly in one stretched memory cycle, and uncorrectable errors, such as double-bit errors cause a distinctive kernel panic, machine check.

That is not a kernel panic, that is an Application panic. Its report is only interesting to the developer.

If a kernel panic occurs, information is added to a log file in the folder /Library/Logs/DiagnosticReports

.

As the problems started after the machine was physically moved it could be that has caused the problem. While it is less common on a Mac Pro I would check the power lead at both ends to make sure that it is firmly seated and undamaged. As an example the old style Mac mini had a power connector that was prone to being pulled out by the weight of the power adapter.

Similarly due to being moved internal components could have become partially unseated. I would therefore when it is turned off open the case and make sure the RAM chips are pushed in firmly, the video card is also checked and pushed in to its slot and any internal cables especially the video power cables and fan cables that you can get at are also all checked.

If the problem only happens when you are heavily pushing the CPU usage e.g. when doing a render then overheating could be an issue if a fan has failed or is as above not connected properly. For programs that heavily push the use of the GPU chip i.e. video card then if the video card does not get enough power it will shutdown. A video card draws up to 75w of power from the PCIe slot but might also need additional power from one or two PCIe power cables. The Mac Pro supports a maximum of two 6-pin power cables each of which can also provide 75w giving a maximum total therefore of 215w. If one is not connected correctly to the video card or the video card needs even more than 215w then this could cause a problem.

It would also be worth running Disk Utility and checking the SMART status of the hard drive(s).

Is the northbridge chip temperature "crazy-high"?

This can be caused by failure of the retaining pins. It is simple to check for on a one socket (4 or 6 -core). After powering off, slide out the processor shelf and try to wiggle the chip in the center of the board. The northbridge peeks out from under the adjacent processor heatsink. It should seem solid. If it is obviously wiggly, you have problem.