Kanye West and Kim Kardashian Celebrate North's 5th Birthday in NYC

North West is kicking and screaming into old(er) age ... just like the rest of us.

North didn't look thrilled about turning 5 on Friday -- not at first, anyway -- but Kanye and Kim Kardashian West carried on with her party in NYC. Dad carried her out to the car, and through what looked like a brief tantrum.

She eventually settled down -- in her super cute traditional Chinese dress -- as the fam and some friends hit up the Polo Bar for dinner, and more importantly ... killer birthday dessert from Sugar Factory!

Now, we know serving up cakes is nothing new for Kim -- she's been doing it for years -- but, the multi-layered one she sliced into for her daughter's party was spectacular ... complete with candy in the center! Just watch. (Diabetics might wanna look away)