Strength (Athletics) is indeed the appropriate check to call for when a PC tries to jump an unusually long distance, and the action has a chance of success, a chance of failure, and a cost or consequence for failure. Personally, I don’t find “try” to be an approach with a chance of success at the goal of “jump farther than my Strength allows.” To have a chance of success, the player needs to propose a course of action that could reasonably lead them to covering more ground with the jump (such as using a springboard). Though, I do believe that the way this rule is written does leave it up to the DM’s judgment to make that call.