I have been in a monogamous lesbian relationship with my girlfriend for 5 years, when about a year and a half ago, I realized that I am both bi + poly. I did a lot of research + soul searching, and then 8 months ago I told her how I was feeling. It didn't go well, we swept it under the rug and I've tried very hard just to sit on these feelings. I realized now that for me, it's my identity and likely a deal breaker: how do I have this conversation again, knowing it will end in a breakup?
If you know it will end in a breakup, there's not much else to be done, or scripted, or strategized. It's heartbreaking and painful to end a 5 year relationship, but it's understandable, and normal, to have to do so after learning about a dealbreaker.
You let her know that you've tried monogamy with her, and you've tried to 'sit on' these feelings, and now you have 8 months worth of information about how it feels and whether it's working for her. You explain that, unfortunately, you've realized this is a dealbreaker, and so you need to break the deal, and leave the relationship. This conversation will suck - breakups always do. But it's important and necessary.
Try not to frame it as "you wouldn't let me date polyamorously, so I have to leave - this is your fault." It's no one's fault, it's just how the universe has shaken out. You two were good together for five years, and nothing can change or erase that, but you're not good to continue dating into the future. Give her the space she needs to grieve, and rage. Best of luck.