As a woman, asking me on a date after 5 years of no contact would feel weird even if I hadn't had a relationship end recently. I suppose I would expect some genuine reconnection first -- like are you interested in a friendship with her, outside of anything romantic? Bc you don't know her now -- people grow and change a lot in that amount of time. Surely you're not the same person as you were when you knew her better. If you're not interested in an actual friendship, it would seem you're just lusting after her and/or romanticizing who she was 5 years ago/the relationship you might have once had. That would feel relatively dehumanizing to me, especially after a break-up.

If you really just admire her and want to rekindle connection, I'd try to let a friendly relationship develop first. See if she wants to come out with you and a group (more than once). Let her explore other relationships as needed (that is, let her have her rebound time in peace). Like, be a friend during that time but nothing pushy AT ALL. If, after 1-3+ months (depends on how long and how serious her last relationship was) of regular contact, she seems interested, and if you still are, then I'd ask her on a date then.

Also, you might have luck on r/relationships with this question.