Hello, thanks for your question today! I am Dr. Drew, and I am a licensed veterinarian. I'll be happy to help you in any way I can.
Continued bleeding for 5 months is definitely NOT normal,
and I would be quite concerned about some sort of hormonal imbalance occurring, causing her reproductive tract to fail to return to a normal "anestrus" state after cycling.
I disagree with your vet's suggestion to wait and have it stop eventually -- perhaps for 1-2 months I could possibly go along with that,
but after 5 months, this issue needs to be investigated!