I am slightly confused about how far a PC can jump in combat. On page 182, the PHB defines the mechanics of the long jump:
When you make a long jump, you cover a number of feet up to your Strength score if you move at least 10 feet on foot immediately before the jump. When you make a standing long jump, you can leap only half that distance. Either way, each foot you clear on the jump costs a foot of movement.
The subsequent description of the high jump is essentially analogous with the Strength score replaced with the Strength modifier. However, it also features the following addition:
In some circumstances, your DM might allow you to make a Strength (Athletics) check to jump higher than you normally can.
Since this is explicitly spelled out for the high jump and no similar mechanic is mentioned in the context of the long jump, I'd be inclined to infer that being able to jump farther by making a successful Strength check is not intended by the game designers. However, on page 175, the PHB explicitly lists the following as an example of an Athletics check:
You try to jump an unusually long distance
Note though, that it is not specified whether this pertains to horizontal or vertical distances, so it could be that this is just a re-iteration of the above-mentioned rule about high jumps. Given the vocabulary used in the distinction between long (horizontal) and high (vertical) jumps, it seems reasonable to assume that this sentence is talking about a horizontal distance, though. Still, there is no explicit mention of exceeding your normal maximum length for a long jump.
Unlike in this discussion, I do not care about whether or not it is possible to split up the jump over several rounds. For the sake of simplicity, let us only talk about crossing a horizontal gap that is longer than your Strength score but shorter than your Movement minus a 10 feet start. Let's use the (vague) nomenclature in the PHB and call a jump over such a distance an unusually long jump. My question then is:
Is it, by RAW, indeed possible to perform an unusually long jump by passing a Strength (Athletics) check?
I have the following context in mind: When playing on a grid, the relevant jump lengths are usually multiples of 5 feet. If for example a PC has a Strength score of 8, that effectively means they can jump only 5 feet. In my opinion, letting them jump 10 feet instead should obviously not come for free, but it also shouldn't be too big a deal. If someone could refer me to an official source that offers clarification on that matter, I'd be very happy. Maybe some rule book even features a table for suitable DCs for given jump lengths. I know that this exists in DnD 3.5, so maybe there is hope for 5e as well.