This is a complex topic.
When you are exercising, you are burning both fat and carbohydrate. If you are exercising easily, the bulk of the energy is coming from fat. As you start exercising harder, you will hit the limit of the energy that can be supplied through fat metabolism, and the extra energy will be supplied by carbohydrate metabolism. If you are working very hard, the majority of the energy comes from carbs.
To answer your specific question - whether 5 minutes at high speed burns more fat than 30 minutes at a lower speed, the answer is "probably not", for a couple of reasons.
First, even if you burnt all fat, that would mean that you would have to be working 6 times as hard to burn the same amount of energy in 5 minutes as in 30. That would be a very big spread in effort; if you are working pretty hard at both durations, it would be rare to work twice as hard on a 5 minute (a more typical ratio is perhaps 30% harder).
Second, the majority of the extra energy you burn at 5 minutes would come from carbohydrate, not fat.
So, if you are looking for burning more calories during a workout, a longer workout will nearly always burn more calories than a short one. If you want to lose weight, you should care about the overall number of calories you burn, not just the fat calories you burn.
However, higher-intensity workouts do burn more calories per minute, and can also burn more fat calories per minute. They will also burn additional calories at a higher rate after the workout is over.
A caution: High intensity workouts are harder on your body, and it's easy to overdo it.