Okay, well, if you're going to be in the gym every day, then there's no reason that spacing things out will hurt anything more than your overall plan will, anyway.
Just do one core lift per day or so.
Monday - 5 sets of 5 bench press
Tuesday - 5 sets of 5 barbell rows OR some kind of heavy pulling
Wednesday - 5 sets of 5 standing military press OR db press
Thursday - 5 sets of 5 pullups/weighted pullups if you can do more than 5 reps of bodyweight
Friday - 5 sets of 5 dips/weighted dips if you can do more than 5 reps of bodyweight
Saturday - 3 sets of 5 leg press, 3 sets of 5 hamstring curl, 3 sets of 15 weighted incline crunches
Sunday - rest
I mean, it sucks, but it's about as good as you're going to do with the limitations you've given.