I have a set of path lights that specify 5 watt maximum for replacement. What happens if I put a higher wattage bulb in there? Can it burn my system up or cause a fire?
Yes and Yes. The maximum wattage is probably to prevent buildup of heat, and using a value over the limit could cause issues: melting the fixture, burning the bulb out, or potentially causing a fire. You will also cause a higher current to be flowing through the wiring, which could be an issue.
Note that the only important value is the actual wattage of the bulb, not the "watt-equivalent". E.g. if you switch to an LED bulb you may be able to get much more light while staying under 5 watts.