My dad and I have done Chicago-Providence in 15-16 hours on several occassions, and he's done it alone. I would say know your limits, be willing to stop and sightsee a little bit, sleep a fair amount. Driving while tired is incredibly dangerous. But the trip can be fun and exciting. Obviously LA-NY is longer, but 5 days is do-able.
Have a great trip!
Have a great trip!