I know Drow love their sapient slaves, but what about less intelligent creatures to keep as pets or livestock, or other purposes. Is there any official word on this for 5e or even previous editions?
The Forgotten Realms Wiki1 page for the drow contains a section on animals which list a number of different animals raised by the drow, including sources for where those animals are mentioned, in most entries and span several editions and different articles. Referenced animals include bats and dire bats, Cavvekans, Lizards, Rothe, shriekers, snakes, spiders.
One notable article of interest is the Drow Pets and Animal Companions article which seems to have been taken down from the wizards site (still viewable through the webarchive link)
1. Note that this is a fanmade site and not official, though it references official sources
The Drow raise spiders.
The Drow description in the Monster Manual states:
The drow raise and keep giant spiders to help protect their cities against intruders, even as they drape those cities in beautiful webbing, creating a gossamer snare to catch flying enemies that would otherwise soar over the walls.
Since they worship what is essentially the Goddess of Spiders, Lolth, it makes sense that they would raise arachnids and utilize their venom, silk, etc.
Additionally, the monster manual says about Giant Lizards:
A giant lizard can be ridden or used as a draft animal. Lizardfolk also keep them as pets, and subterranean giant lizards are used as mounts and pack animals by drow, duergar, and other Underdark dwellers.
Besides the answers given I wanted to add another source for Rothé, a type of subterranean oxen used as cattle of some kind. The prologue to R.A. Salvatore's book Exile seems to indicate that the protagonist Drizzt kept these as a source of food:
The hunter watched the basilisk pass as he had watched it earlier that same day. The eight-legged monster was the intruder here, coming into the hunter's domain. He had witnessed the basilisk kill several of his rothé - the small, cattlelike creatures that enhanced his table - with its poison breath, and the rest of the herd had fled blindly down the endless tunnels, perhaps never to return. The hunter was angry.