Why doesn't my house get cooler than 80 degrees with the ac on?

Even after setting the temperature to 65, the house does not cool any less than 80 degrees. An AC technician looked at it and told me that maybe it hasn't been used for a long time and then he changed the air filter. I've been using it for a whole week now for more than 12 hours a day and the temperature only gets as low as 80 degrees. It does utilize a "central air" cooling duct throughout each room in the house, but it doesn't seem to be enough. I don't want my bill to sky-rocket this month because the AC unit is not working efficiently. What's going on and what do I need to do? ( oh yea, the house was built in the late 70's to early 80's, and the unit is located on the roof. Some drips of water is coming from it too. hopefully that helps you)