Even putting aside for a moment the question of whether or not five years is really all that long (it kind of is, especially at such a young age and for such a brief relationship, but it also kind of isn't, especially when you've got this kind of romantic trauma hanging over you), moving on from losing a lover doesn't have to mean finding a new lover. It means finding a way to live a happy life without the one you lost instead of wallowing in that despair.
With that in mind, I think Shizuku is doing well. Not perfectly, perhaps, but she's come out of her shell, she's found something that she thinks she wants to do with her life, she's got a reliable support network built around the shared love and loss of Kaori, and the love she still feels for Kaori is a source of happiness and inspiration and not something on which she's harmfully fixating. I see the proposal as being less a matter of "I want to marry this dead girl" and more a matter of tying up a loose end by doing something she wanted to do while Kaori was alive but wasn't able to, making "I would have married you" something more concrete than just a thought she kept bottled up. Rather than stagnating and holding on to Kaori, I think that's a part of the process of moving on, closing the book on one of the things she regretted not getting a chance to do.
Will she find somebody new to love? It's hard to say. I think her chances are relatively slim, being somebody who will almost certainly always be a little socially awkward and that making it hard to meet and fall in love with people, but I don't get the impression that she's closed herself off to being happy with somebody else. She just doesn't feel the need to look for a new love yet, and that's fine, so long as she's still living life fully and healthily.