It's possible that a 5000-watt generator would be able to run a sump pump, but it would depend on a few factors such as the specific sump pump's wattage requirements and startup surge. If the sump pump needs more than 5000 watts to start up, the generator wouldn't be able to power it. It's also worth considering that a sump pump would likely only need to run for a short period, so a generator with a smaller wattage rating may be able to power it for the duration of its use.