Firstly, the five bars are only telling you the data is being shipped to your computer efficiently, in other words the router is well sited and broadcasting a good signal.
The parlous Internet speed is down to your ISP although they'll probably try to blame you. Do you have a filter on the telephone line to the router? If you have more than one in the same line, take one out. When you pick up your telephone, do you hear noise on the line?
Can you cable the computer to the router just to be absolutely certain wireless can be taken off the suspects list?