If you're using ASP.Net MVC then your app should also come across to .net core fairly painlessly.
The only real challenge is going from the old webforms with its page lifecycle to the asp.net core. But depending on how the application was originally implemented, that really should just be about the frontend, not the entire app. And of course EF core has changes you'll need to deal with as well if you're using it.
It's by no means seamless, but MS did the best they could to maintain compatibility between the two, and you only do it once.
It should also be noted that .net framework is almost 20 years old. Doing something like this once in a 15 year period is a far cry from Laravel's every 6 months or RoR's 2-3 year cadence. IOW, it's not optimal that the divide between framework and core exists, but it's a far better story than Laravel, RoR, et al.
> And who's to say .net core doesn't have any breaking changes in 5 years, are they guaranteeing not to do any breaking changes at all to the framework?
ASP.Net core is literally just a set of libraries. You'll be able to run those on the modern version of .net in 10 years from now. We know this because it's what they did with asp.net. An application built on asp.net 1.0 will work on 4.8.