An ability check must necessarily be tied to a fictional action since the function of an ability check is to resolve uncertainty as to the outcome of the task. A player can always try to have the character jump further, but he or she is obligated to offer the reason why that's even possible.
Sure, but the reason might simply be "I know I can't clear this comfortably - it's further than the gap I jump across every morning when I'm training! - but if I give it my all I might just make it!"
The idea that, by default, the distances a hero can try and jump either fall into the
will automatically make it category and the
can't possibly make it category isn't that appealing to me, and on my reading of the 5e rules is not mandated by them.
People will differ on whether the proposal of "take a deep breath and give it the ol' college try" is sufficient to boost the character's normal jumping distance.
Is it sufficient or not? That seems like something uncertain - and hence that might aptly be determined by a check.
Are you playing D&D 5e yet? In past discussions, you had not. I recall you mostly played D&D 4e (which is quite different from D&D 5e in many ways) or Burning Wheel.
I'm not playing 5e, but this thread came up on a forum front page and the question of how actions should be resolved in various systems is something I find interesting.
The last two sessions I've GMed have been Prince Valiant. (You can read about them
here and
here if you like!) The basic approach to resolution is not different from that which you advocate for 5e - player declares what his/her PC does, and GM stipulates check required (if any) and difficulty. (Unlike 4e there are not resources whose deployment is senstiive to the making of checks; and unlike BW there is no system of advancement contingent on making checks with a particular ability; so calling for checks isn't really a player-side thing.)
I'm running it much as I've been running Classic Traveller (another system I've been running a bit over the past year or so): say "yes" when nothing much is at stake and the fiction doesn't make success terribly improbable; otherwise set an "objective" difficulty (which contrasts with 4e or Cortex+ Heroic - the latter another system I've been running quite a bit recently) and see how the check plays out, with BW-style "fail forward" narration of failures.
Asking to make an ability check is asking for a chance to fail, and the d20 is famously fickle. The smarter play in my view is to describe what you want to do while making an effort to remove uncertainty as to the outcome and/or the meaningful consequence of failure.
I find this very reminiscent of classic D&D or OSR-style play. I feel that it tends to push play in the direction I mentioned upthread - very operationally focused, with a principal consideration being external factors that will allow the character to succeed.
I prefer using "say 'yes'" as a device to manage dramatic pacing rather than as a response to tactical planning, and to use "fail forward" to manage the outcomes of failure. It's also the case that it's a long time since I've run a system with a "notoriously fickle" d20 (4e has the illusion of being such a system, but there are so many player-side resources for generating post hoc boosts, retries, etc that it really isn't) - BW and Prince Valiant are dice pools, Classic Traveller is mostly 2d6, and Cortex+ Heroic is very complicated dice pools with a lot of player-side manipulation as well.
Because of the way 5e strongly demarcates "mundane" checks and "magical" spells and class abilities, I suspect it may be hard to play in the style I prefer, which is one reason why I don't play it. But on this particular issue of a character jumping further than s/he easily can, I think drifting it in that direction in the way that I've described (following [MENTION=467]Reynard[/MENTION]'s description) is not that hard at all. (And in lieu of any sophisticated "fail forward" in the event of failure, if the PC is 14th level as Reynard suggested then the hp mechanics will probably carry that load.)