It really depends on your goals and programming. The answer could be yes or no.
With my current routine, for example, I dead lift, front squat and bench press three times a week, however, I only complete 10 reps of each lift per session (broken up into 2-3 sets, rarely more than 85% 1 RM).
Without getting into the fine details of my current program, I'm mainly targeting strength gains (borrowing from some of the core concepts of Dan John's "Easy Strength" musings). In the said routine, I could care less about hypertrophy.
If you're targeting hypertrophy (muscle growth), completing a high volume of reps, and/or approaching near failure during sets, you could find yourself in an "overtrained" state pretty quickly (though, as Daniel implied, you'll probably get injured first). In that case, I'd strongly consider completing heavy, compound lifts (ie DL, Squats...) once a week, and work from there.
It's hard to completely answer your question without some more details, but if you're really concerned with overtraining prevention, get yourself an HRV (heart rate variability) monitor, keep a log, and go big when your body tells you it's ok.
I see you added that you're doing a 5x5 (sorry if I just missed it the first time around).
You could do a 5x5 approach over four days if you wanted, and complete big lifts, like DLs and squats, twice a week. If you're employing this method, a key element to consider is how you progress the load in between sets. Take this guy's program for example (the second program of the two):
He builds 10-15% each set, until he's finally lifting near his 5 RM in the final set. He does his over 3 days, but you could easily spread it out over 4-5.