Your tap water is not that bad if those readings are correct...
Ammonia 1ppm
Nitrite 0ppm
Nitrate 5ppm
???
Not bad at all so long as you use a water conditioner that temporarily detoxifies the ammonia, and I would use a little extra.
Your pH could be an issue as nitrification stops at a pH of 6. Have you tested the tap water pH after it has gassed out for 24 hours in a cup?