I'm not an electrician and I don't even play one on TV; that said ...
It seems to me that if you used aluminum conduit for the 120v, the conduit would provide enough shielding that there would be no radio frequency interference with any Cat-5 cable that might be in the neighborhood.
That said, personally, I would dig one trench, use aluminum conduit and then use Cat-5 direct burial cable (I'd even zip-tie it to the conduit). If I were really concerned about RF, I'd upgrade the Cat-5 to FTP (foiled twisted pairs), which would then provide a secondary shield.
I would not dig two trenches.
\dmc
PS: And yes, it only took one instance of pulling just one Cat-5 inside a wall for me to never make that mistake again (in my defense, I did pull two cables but one was for POTS and I should have pulled three).