My accord 2005 vibrate drop idle and off on reverse gear, what should be the cause?

Your accord is slipping out of gear..check it one more time..

Buy new mounts, used ones are cheap but usually don't last or are worn also.

moving or not?
sure related.
but moving or not, is a big deal. here.
if brakes set and it vibs in drive , that is engine misfire,
engine shakes,
ever tune up the engine this decage or at last 60k miles?

Possible dirty throttle valve and idle speed control valve.

Throttle Body Cleaning on vehicles without electronic throttle control (most 2003 and down)

You can in most cases repair this slow speed stall or unstable idle by cleaning the engine throttle valve and the idle speed control valve using a product called CRC Spray Throttle valve cleaner. Spray the cleaner into the air intake of the engine with the hose removed from the throttle body, the engine will try to stall so hold up the idle speed manually. Once you have used up about 1/2 can of the cleaner stall the engine out while spraying and turn the key off, disconnect the negative battery cable for 5 minutes and then reconnect and drive the car for a about 25 miles of varied driving modes. If this doesn't cure the problem you may need the fuel injectors professionally cleaned by the dealer service dept.

Your motor mounts are either worn out or broken causing you to feel the vibration from the engine. Another possibility is that your exhaust pipe is touching the body somewhere.

a low idle can cause this fault but only when the car is not moving, may need tune up. a broken engine or transmission mount can also cause fault, car will also thump as it goes up through the gears. last but not least, if the vibration is there all the time when driving the inner C.V joints may be worn, more noticeable under load & acceleration. this should help you diagnose witch fault to look at

Have your motor mounts checked very soon. This only shows in reverse because reverse causes a backward torque than the engine does in forward gear.

Is the engine light on? If not, It'probly time for an idle air control valve. Also check the motor mounts. Put the car in drive, hold the brake and give it some gas. Do the same thing in reverse. If the motor moves more than a few inches, you may have a broke motor mount.(you watch the motor, let a friend work the gas)

your motor mount is probaly bad and needs to be checked

check your rear engine mount.

Delroy - Jamaica