What is this noise on this honda?

My mother has a 2005 Honda CRV and she has had it since it came out. She has never had a problem with it but now when she's at a red light then takes off there's a bad noise. It happens in the rear of the car. The noise is sort of a clicking noise.

Rear dif needs an oil change with special honda rear fluid.

Both of the rear half shafts (CV shafts) need to be inspect for torn boots. If any the boot is torn, that CV joint or the whole shaft need to be replaced. That what I've seen on some of the CR-V for the past five years.
There's a TSB Honda issued on CR-V for a moan/ groan noise from rear differential when making a sharp or tight turn at low speeds and the probable cause is contamination in the rear differential fluid. I don't think it apply to your case but I mentioned for your information for future reference.
The second TSB is owners complaint about a squeak or rattle from rear of vehicle. Some 2005-2009 Japanese-built CR-V sport/utes may produce an annoying squeak or rattle from the rear while being driven.
One likely cause of the noise, reports Honda, is the metal hook or bracket at the top of the rear shock making contact with the vehicle body. Removing the rear wheelhouse and bending the hook or bracket away from the area where it makes contact with the body is the simple fix.
For your information, both the hook and bracket are nothing more than aids that helped in the assembly process at the factory.
So check it out: Clicking noise is most likely like I've mentioned in the beginning of my answer: Check the rear CV shafts. HTH
Edit: I've included one of the TSBs cause YA only allow one media to be included in an answer.