Most Non-Combat challenges are solved through stat rolls; characters must roll 2d6+ a stat to perform abilities related to the stat.
CON is focused on physical endurance and some rudimentary forms of reality shaping. Running for a long time or having your beliefs suddenly thrown in to question would require a CON check.
CRE focuses on physical skill, precision, dexterity, and analysis/knowledge. Lifting something heavy, dodging an attack or knowing some trivia requires a CRE check.
CHA deals mainly with diplomacy, trickery and concealment. Convincing people to do something or hiding from something requires a CHA check.
While Roleplaying and Puzzle solving is encouraged, Non-combat difficulty checks are not intended to be a major part of the game. Skill rolls are there to encourage an element of chance for when the DM believes it is necessary.
5 is required for low difficulty [but risky] actions, only to be used on philosophers with less than 3 in a stat.
10 is medium difficulty actions
15 is high difficulty actions
20 is for nigh impossible actions