You've been together five years, and now you are moving in together. I'm sorry, but THAT is commitment. Why your mom doesn't see that, I have no clue. She just has to see you are really happy, just give her time. She doesn't want to let you go, but she will......eventually.
I've been with my boyfriend for 9 years, moved in with him after 5 months of dating. I do not see wedding bells in the future and I'm fine with that. Everyone else seems to have a problem with it, but I just tell them....I'm happy! That's all that matters.