One of the things you need to be very aware of, that while they are pets to you, they are considered livestock to the state. There are laws that need to be followed. Thing is, your birds in a totally different climate, can be carriers of a disease that is non-existent in the new place - those birds will have no protection to it at all.
Or vice versa is true too, there may be a disease in the soil that birds raised in it, get natural immunization to it. New birds exposed to it can become very sick and die. Birds traveling for 5 days will be highly stressed and therefore very susceptible to any disease.
Check with your local laws, the laws into the state you traveling through, and the state that you are making your new home. It is vitally important that you follow the laws. If you were stopped, for whatever reason. And you do not have the correct paper work proving you have healthy birds - you could have them confiscated and depopulated. Agriculture takes these laws very seriously.
The above poster while acting generously is risking a great deal. I am not a big believer in quarantine, but I only get local birds, birds raised like mine that have not been exposed to other birds. I would not want to take your birds temporarily due to the incredible risk to either your flock or mine.
Mrs K