One problem related to manifold/header/muffler/tail pipe has been reported for the 2005 Honda CR-V. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2005 Honda CR-V based on all problems reported for the 2005 CR-V.
I stopped at a gas station and got gas. I turned off the air conditioning before turning off the engine, as always. Got in and started the car, turned on the a/c, and it blew hot air. I kept trying it all the way home and nothing but hot air. The next day I noticed a ticking sound under the hood when it was idling. Mid summer, but no money to bring it in. One month later the ticking under the hood got progressively worse so I took it in for a free a/c check. Turns out the whole a/c system needs to be replaced (estimate $1000) compressor w/clutch, orifice tube, receiver/dryer, and re-charge. Thousands of online complaints and potential hazards. Ticking could be caused by all of this, or loose valves, exhaust manifold, etc. . . Contacting Honda, to see what they can do. . .