Here's the deal guys, I recently decided to compete in several BJJ and judo tournaments that are coming up (iv never competed in either sport before) and up until now iv just kinda taken it light with my training. Now however im trying to kick it into high gear to get ready. Im following the bill star 5x5 for my strength training and doing randori/rolling for my conditioning. I only have 3 days a week that I can really commit to training so iv been lifting in the mornings and then practicing my judo/ BJJ at night on the same days. My problem is that iv started suffering injuries pretty frequently, and since my diet and sleep patterns are good I think the problem is in the way im training. So my question to you is what could I do to improve my schedule? 
What type of injuries? Are you getting hurt during randori/rolling, or more the wake up in the morning wondering why something suddenly hurts? How old are you?
Im 23. The injuries iv had are mostly pulled muscles, iv pulled my hamstring and calf doing randori, strained something my back doing squats even with a belt on. Now I have what feels like an AC strain, I go caught in a kimura when i was rolling the guy thought I had a hold of my gi so he just slammed it on, although it didn't really start bugging me until 2 days later when I was doing standing overhead presses.
Doing the 5x5 along with hard rolling is a lot of working out, particularly if it is a significant increase in the ammount of exercise from what you were doing when you were "taking it light" with your training. If you have a tournament in the near future (next month or two), I would consider bagging the lifting for now and focus on cardio/randori/rolling; and then try to add back the weights after the comps. In general, if you start getting more injuries shortly after you ramp up your workouts, you are probably overtraining. I would think about reviewing your planned program with a good trainer or strength/conditioning coach if any of your gyms has one.