...I believe it's required.

You could grab a cab and go to poipu beach and the spouting horn and then get to Duke's for bite to eat before your flight. Very do-able in 5 hours.

I'd suggest a cab to the Marriott in Lihue and hang out at Duke's Barefoot Bar for a drink and a view of the beach. Then explore the local area for some last minute gifts and then maybe a meal at Duke's upstairs or even across the street at Kalapaki Joe's.