What's the maximum spec of processor the Dell precision 390 can utilise?

Here are the builds on that system.
http://www.userbenchmark.com/System/Dell-Precision-WorkStation-390/1890
I'm seeing Q6700 there. But if you're looking for adventure I would try the QX6800 SLACP.65nm 266fsb 2.93GHz.
https://en.wikipedia.org/wiki/Dell_Precision
That's what I ran in the Dell dimension E520 from the same era. There are some links in my sig. about this mod.
If yours turns out to only support 2 core CPUs then the X6800 would be the maximum CPU. The latest BIOS update is always good for CPU support.
https://www.engadget.com/2006/07/28/dell-precision-390-workstation-goes-core-2-too/