Jim Schmitz, former Olympic lifting coach offers good insights here.
The other factors of running that might influence your lifting are the
volume and intensity of your running. Sprints can be more stressful
than jogging and long distances are more depleting than both. Running
hills, stairs or cross country is the most demanding and will
definitely fatigue your legs a lot. Whichever form of running you do,
all can affect your lifting depending on how fast, hard, and long you
run. So be aware—if you want to lift heavy the next day, run easy to
medium the day before.
He also talks about backing off on either prior to competition, or when hitting PRs... in which case, when you're in the advanced phase of SL 5x5 (nearing 300lb squats) you'll probably want to dial back the running if you want to progress on the lifts.
Running won’t adversely affect your weightlifting—and vice
versa—provided you do it intelligently and systematically, and both
are definitely beneficial for overall strength and health. Remember,
though, if you are peaking for a competition (or planning workouts for
some PRs), taper off your running—or weightlifting, if that’s the
case—as the competition date draws near.
If you're using the app with SL 5x5, it'll auto deload the weight for you if you fail to lift it three workouts in a row. It also tracks your progression. Remember that even the best trainers can't make predictions for you: You know YOU better than anybody else. My recommendation is if you find yourself deloading fairly frequently on squats/DL but aren't near a 250-300lb squat or 300lb DL first look at your diet: Are you actually eating enough calories and protein for your muscles to build? Are you getting 8hrs of sleep? Getting these wrong will hurt you far more than a little cardio. If you ARE getting these things, are you sure your lifting technique is correct? If not that, THEN maybe look at running less frequently or try Jim's suggestion on interval training as a replacement for C25K:
Interval training— where you run for a certain distance or time and
then walk for a certain distance or time—is a great running method for
weightlifters. I have found interval training to be tremendous for
developing one’s cardiovascular fitness, which then helps your
recovery from weightlifting workouts. I have also found that running
20 to 30 minutes (or 2 to 3 miles) two to three times a week on
non-workout days, or after light-to-medium weightlifting workouts, has
no adverse effect on one’s lifting.
C25K as I recall, is exactly that: interval training working up to Running 20 to 30 minutes. If you keep it on off-days, I think you'll be fine. Adjust diet, sleep, and technique first on your lifts.