Individuals within a species often vary in both their problem-solving approach and ability, affecting their capacity to access novel food resources. Testing problem-solving in free-ranging individuals is crucial for understanding the fundamental ecological implications of problem-solving capacity. To examine the factors affecting problem-solving in free-ranging animals we presented three food-extraction tasks of increasing difficulty to urban common brushtail possums (Trichosurus vulpecula). We quantified two measures of problem-solving performance: trial outcome (success/failure) and time to solve, and tested the influence of a range of potential drivers including individual traits (personality, body weight, sex, and age), mechanistic behaviors that quantify problem-solving approach (work time, functional behavior time, behavioral diversity, and flexibility), and prior experience with the puzzles. We found that mechanistic behaviors were key drivers of performance. Individuals displaying greater persistence (higher work and functional behavior time) were more likely to solve a food-extraction task on their first attempt. Individuals also solved problems faster if they were more persistent and had lower behavioral flexibility. Personality indirectly affected time to solve one of the three problems, by influencing time allocated to functional behaviors. Finally, adults solved the most difficult problem faster than juveniles. Overall, our study provides rare insight into the drivers underlying problem-solving performance of wild animals. Such insight could be used to improve management strategies and conservation efforts, such as food or bait deployment, tailored to suit the foraging innovative abilities of target individuals in new and changing environments.