"Here" on my own property I'd probably do it into heavy grade PVC. Haven't a clue what the code (if any) is where you are, or even WHERE you are. Burial grade wire doesn't require conduit but I might do it just to do it right, and laying PVC (or even just the wire) with a subsoiler is a lot faster than digging a trench. I have a tractor though so that part'd be easy. How deep? I'd be quite happy with a foot for conduit, maybe 4-6" for the plain wire. Again, that's "me" and "here". Haven't a clue what the code says "there" and I'm not a professional cctv guy anyway, although I pretty much have my doctorate in redneck engineering. If someone shows up with an actual certificate in something relevant and voices an opinion then listen to them instead.
Not quite sure what you mean by "Ubiquiti Cat 5 wire" though? Leave out the Ubiquiti and it's just regular old UTP (unshielded twisted pair) which is what Cat 5/6 wire is.
My first choice would be to avoid the hassles/expense of trenching altogether and use the PLAs (power line adapters) unless you have pre-existing conduit (still don't remember a yes or no to that part) and are willing to take the chance that running the cat 5 too close to the AC wires won't bugger things up. Supposed to be 6-8 inch separation or so to avoid problems. The powers that be say no to long parallel runs when right next to each other. You might even pass a charge into the UTP from the AC line and fry something expensive rather than just have unreliable data. Then Nanostations second. Then trenching either whole hog with subsoiler and conduit or a 3pt mounted disk and just burial grade wire. Although I'd usually choose cat 5 somehow as a first choice, in this case it's possibly 3rd choice. Maybe a distant 3rd depending on what kind of yard you'd be ripping up and the difficulty of blending in the conduit and getting it in the house, although trenching bare wire isn't a terrible idea and is a lot easier the first time.
$40 for a pair of decent PLAs, maybe $70 for a PoE switch, $40 for a waterproof project box, some short patch cords, plus your cameras and you're golden with an hour or maybe three of install time depending on how you want to mount your cameras. Easy peasy fast and easy. For Nanostations turn the $40 for PLAs into say $120 and all the other parts and a bunch of time figuring out how to program them. They don't come with directions and I bet the YouTube videos you find won't match what your firmware menus look like (they've changed over the years since most of the videos were put online and the last I checked the new format didn't have matching videos) so it'll take a fair number of hours to get them talking to each other. Not a big deal but it does take time to learn the intent of the videos and adapt it to what your firmware shows. Then the big time, expense, and effort unless you're set up for it- trenching in new cat 5 cable and hoping you don't cut the existing power cable going out there and really getting into a mess, although you might be happy with tucking some burial grade cat 5 just under the sod of your lawn after cutting and prying open a long line with a spade. Jump on the spade, pry open a wedge, move the spade, repeat. Might hit it with the lawnmower after a year or so of frost heaves or might last a looong time if the roots mend quickly and tie it down under. Don't forget to run an extra strand for insurance or futureproofing. Even using a spade try and be sure you don't cut the existing line going out there. Stranger things have happened than have people just tuck unprotected indoor grade 14/2 into the sod and run it out to a lightpost. Best case is you have to replace that line too. Worst case is you get a bad or fatal shock.