Once you pick up the orb (Or apport it, I believe) the orb run starts, and random demonic enemies will spawn in... randomly. It also makes a huge noise, and cuts your stealth in half.
So, the first concern when picking up the orb is the stuff already on the level, as anything nearby is going to come investigate all the noise. Of course, if you fought your way to the orb, then at least half the orb chamber is clear already, so you're mostly concerned with what comes out of the other half. On top of that, stuff is going to randomly spawn in.
The solution to this is not to stand and fight, at least, not if you can help it. For the most part, your first move after picking up the orb should be to haste yourself, via potion, wand, or spell. Then start running toward the upstairs. Zot 5 is the most dangerous part of the orb run, you want to get off this floor ASAP.
Now, if things start getting dicey (for example, smiting or hellfiring demons all over you) don't hesitate to teleport. Typically at this point of the game, you're going to have lots of teleport scrolls, and maybe a wand or two. Basically, teleport if too many enemies are around, and then make your way to the nearest staircase. Repeat if necessary.
Once you get out of Zot 5, it gets a bit easier typically, because the staircases are generally going to be easier to get to. But use the same strategy as before, haste to get away from dangerous enemies, do as little fighting as possible, and if things get ugly, teleport. If you've got wand(s) of digging, don't hesitate to use them to make a shorter path to the staircase.
It sounds like you got a particularly tough orb run, which is too bad, it sucks to die there. But at least you should know it's not usually too hard. Usually if you just keep moving, you can just walk right through each floor all the way to the top.
I would disagree with advice to apport the orb to the staircase, I believe the devs changed it so that starts the bad stuff just like picking it up does, so there's nothing to be gained by apporting it.
You can pre-dig paths for the orb run if you want, I never have, but if you're feeling especially paranoid it might at least give you a little peace of mind. Just realize that bad stuff can spawn in Zot and the depths, and the more time you spend screwing around digging tunnels, the more chance something bad might happen.