$5.77/week doesn't seem too terrible. I don't recall exactly what I paid when I lived in town, but I think $10-$15/month is close.
I have a county recycling center about a mile from my house, so it couldn't be much more convenient for me. I recycle glass, plastic, aluminum cans, steel cans, cardboard, newspapers, and batteries. I have 1 trash can in both the barn and gararge for non-recyclables (mostly diapers from our 1 year old).
I go to the recycling center, which also takes trash at $1/bag, about once a week. I average about 1 large bag of trash (I have the 55 gallon trash bags from Rural King) and 1-2 of my recycling collection bins per trip. It takes me probably an extra 15-20 minutes per week vs. curbside pickup. But, I have the luxury of a owning pickup truck and a very close recycling/trash center. If I lived 15 minutes from the recycling center or didn't have a truck, I wouldn't think much of paying $6/week for curbside pickup.
My folks live in town (Jasper, IN) and pay $1/bag (have to buy stickers to put on each bag) and have curbside recycling. I don't know if their, or my, taxes include a line item for "trash disposal".