Which famous unsolved math problems probably don't need completely new mathematics?

It seems that some famous unsolved problems (at least according to many mathematicians) might eventually be solved using existing mathematical tools, if someone finds the right idea or combination of techniques.

Examples that come to mind are:

• Riemann Hypothesis
• Collatz Conjecture
• Strong Goldbach Conjecture
• Some of the Millennium Prize Problems (maybe?)
• Twin Prime Conjecture, etc.

On the other hand, I've heard that some problems may require entirely new mathematical theories before they can be solved. People sometimes mention things like the ABC Conjecture (before Mochizuki's claimed proof was proposed) as requiring new ideas, whereas Navier–Stokes seems to be in a different category as it may get solved using existing tools ?

So my questions are:

1. Which major unsolved problems are generally believed to be solvable using existing mathematics, but we simply haven't found the right argument yet?
2. Which problems are widely thought to require fundamentally new mathematical tools or theories?
3. Why do mathematicians make this distinction? Is it based on evidence, or is it mostly intuition from experts?

I'd really appreciate explanations in simple language rather than highly technical ones. Thanks!

Author: United_Sandwich581