(1) Although it seems likely that the OS reboot issue is related to your installation (possibly a driver issue), you might consider running Dell's pre-boot diagnostic (ePSA) to check that the hardware is operating normally. F12 repeat-click during boot and select "Diagnostics" from the menu to run ePSA. The test will take a while, but it will eliminate hardware issues.
(2) If this is a standard Optiplex 5050 7th Gen build, the computer's basic specs are: (a) Intel i5-7400 or i5-7500, (b) Intel HD 630 Graphics, (not the optional AMD Radeon R5 discrete), (c) Realtek ALC3234 audio, (d) Intel AC 8265 Wi-Fi + BT 4.2 and Intel i219-V Gigabit1 Ethernet. Could you confirm that your Optiplex is a vanilla build (in particular, no discrete graphics and no third-party hardware added)? If the build is not vanilla, could you let us know the current specs?
(3) Because the reboot issue appears to be intermittent, can you identify any particular process/app you are running when the reboot issue appears, but not running when the computer doesn't reboot?
(4) What Solus version (Budgie, Plasma, MATE, Gnome) are you running? Have you added/deleted any software to the base build?
With that information, the gurus on this board might be able to help troubleshoot.
Edit/Update: I took a few minutes to research the reboot issue you are experiencing online, and discovered a number of reports of the issue relating to Optiplex computers in general. The problem in those cases was related to a power interrupt, in particular power interrupts related to USB-connected Brother printers, faulty/overloaded UPS and so on -- anything that might cause a surge/decrease in power available to the computer. That is something you might look at because the issue is intermittent. I suppose that it is also possible that the computer's power supply or one of the power supply cables is failing, or a connection loose or dirty.
Edit/Update#2: I did a bit of looking this morning, and found additional threads. The threads tag hardware issues for the most part (see "Why does my Dell Optiplex 755 continue to sporadically reboot?" for an example of what I've been finding), but I have also found a few that relate to driver issues. Because the issue arose when you installed Solus, I suspect a driver issue. At this point, I'd suggest three things: (1) run the ePSA to rule out basic hardware problems, (2) run basic troubleshooting (sudo eopkg up followed by sudo eopkg check | grep Broken | awk '{print $4}' | xargs sudo eopkg it --reinstall) to ensure that the drivers installed are in good order, and (3) if all else fails, back up your data and try a clean reinstall of Solus.
As an aside, I'm interested in the issue because I run Dell Optiplex and Latitude equipment exclusively. I have been running Solus Budgie on an Optiplex Micro 7050 (6th Gen Intel vanilla) and (until recently) on an Optiplex Micro 7070 (9th Gen Intel vanilla) for several years without issue. For that reason, I don't think that Solus and Optiplex computers are incompatible in any way that would cause the issue you are describing.
