Good for you for picking up the weight and sticking with it.
5 sets of each exercise is a good number. 5 minutes between sets, however, is a bit much. You should rest about 1 minute between each set of 5. If you want to take 5 minutes between completing one exercise and moving to the next, however, that is fine.
My recommendation for getting the most out of the exercises you're doing is to start focusing more on your chest and back. Your biceps and triceps will get plenty of work moving weight away, and pulling weight towards, your body. Decline/flat/incline bench presses (if your equipment allows for this) and dips are excellent chest exercises. Barbelll and dumbbell rows and pullups/downs are excellent back exercises.
If you made a routine that reflected this, you would get:
Chest day (chest, triceps, front delts [shoulders]
- Flat bench
- Decline bench
- Incline bench
- Dumbbell flies (something to do if you can't adjust your bench)
- Dips (if you can do them, it can take some time)
Back day (traps, lats, rhomboids, lower back, rear delts)
- Bent over barbell row
- Pullups/cable pulldowns
- Bent over dumbbell rows (different stabilizers worked than barbell, feels different)
At home, I would do a chest and back day, rest for two days, and repeat. Eat well and grow!