5x5 deadlift is absolutely fine, but not during the SL5x5.
As Aequitas nails on the head, the Stronglift 5x5 program already includes 5x5 squats, 3 days a week, and as such, your legs, glutes and lower back will constantly be in a state of recovery. Adding a lot of sets of deadlifts on top of this will very likely hinder your progress, as you might never get to reach an anabolic state.
Remember, squats and deadlifts target the same primary movers, but with slightly different ratios of intensity.
However, if you do a program with, say, 1 leg day per week where you do deadlifts, then it's absolutely fine to do 5x5, 3x8, or whatever you see fit.
Keep in mind that deadlift is typically the exercise where you move the largest amount of weight, and people are correct to point out that this is very taxing on your CNS if you do it too often.
Designing a program around deadlifts (example)
Add deadlifts to one day of the week
Consider this leg day, add squats, and vary/alternate which one of them you do first. Accessorize with leg/lower back movements like back raise, leg extensions, leg curls, as these will facilitate more gains on the deadlift-relevant muscle groups
Train at least one other day of the week.
if you only train one more day of the week, make it an upper body day, and make sure to incorporate both pressing and pulling movements, and at least one compound exercise of each category
if you train two more days of the week, make it a pull day, and a push day
There is also the alternative of considering deadlifts on back days, and having a separate leg day with squats. However, if you're unsure, err on the side of caution, and have only one leg day. If you feel super ready to have two leg days (i.e. having deadlifts on back day), then research (or come back and ask for) some tips on that.