Not quite sure what you're trying to go for, but that 5100 will NOT cut after a certain point. Sure, it can take some awesome shots when squeezed to its limits, in perfect lighting, on a tripod, but it's still no 7000 if you know what I mean. Just keep on keeping on and save up to move to FX. That's when you'll really start breathing photography.
I would not agree with that. Higher end model, e.g. D7100 may help ease the tedium in professional environment - faster bursts, faster AF, brighter VF, two cards and wider bracketing, but when you come down to the core shooting, they it is same as D5300 as far as low light and sensor density is concerned. In fact if you take analogy of film era, both have the same film. It is same as claiming that a Nikon FM10 takes better pictures than Nikon F6 with the same film.
Where you have a point is that to shoot extreme sports, you need fast body and a very fast lense, but then you do that when you are either selling (or employed to take) the pictures or extremely rich. For general photography, as long as you have a camera which is in the D3xxx, D5xxx, D7xxx or D6xx there are very few limitations. In fact for landscapes all you need is a lense with corner to corner sharpness at F5.6-F11 and a high MP sensor, on a camera with reasonably low noise at base ISO.
Where the FX score in my opinion is
. Better DR, hence better low light performance.
. Wide angles are wide angles, hence a 24mm prime will behave like a 16mm on DX, and a 14mm as 9.5mm. A distinct advantage.
. Brighter View Finder.
But none of these advantages will give you better images. That is in your hands.