How much will it cost to replace the brakes on my 2005 Honda Civic?

Depends. Are you doing the replacement yourself? Then it would only cost 20-30 dollars to replace the front or rear brake pads. If the rotors need to be turned, if there is any damage to them, you will need to get them resourced or if the damage is too bad, you will need to replace them. If you take your car to the shop, most have "specials" for 99-125 depended on the work that needs to be done. I would invest in a set of metric wrenches and sockets, buy the shop manual for your civic and do them yourself. Good luck.

The cost will depend upon the condition of the rotors-If you have let your brake shoes wear past the rivets, those rivets are scoring your brake rotors-depending on the damage, they can wither be turned and reused or they will have to be replaced. Rotors for you vehicle range from about $70 to $150, the shoes all around another $100 or so....with labor worst case scenario is probably around $350-$400 smackers.