Do you have travel insurance? (You should do if you're travelling internationally!)

Travel insurance policies often have cover for something called "travel disruption" - which includes missing a flight because an inbound flight was late. My policy (UK-issued) does not specify how much time I have to allow between flights before they will cover me, but I gather (from what I've read here) that other policies do.

Five hours between flights should normally be plenty, even on separate tickets. An hour to get your baggage (if there is no interline agreement), go through Immigration and make your way to the check-in desk. Check-in will probably close an hour before the flight, so you have three hours to play with. I wouldn't worry too much - but do make sure you have insurance.