Learn French: Le vainqueur arrive dans cinq minutes. - The winner arrives in five minutes.

This is the core rule for this lesson! Dans tells you when an action will happen in the future (five minutes from now). If you used en, it would mean the action takes a certain amount of time to complete (for example, running a whole race en cinq minutes).

Since this happens in the future, why is the verb arrive in the present tense?

Just like in English, French often uses the present tense for near-future events or things happening on a set schedule. You could absolutely say va arriver (is going to arrive) or arrivera (will arrive), but using the simple present is very natural and common here.

How do you pronounce the qu in vainqueur?

In French, qu almost always makes a hard 'k' sound, never a 'kw' sound like in English. So vainqueur sounds roughly like 'van-kuhr'. It is related to the verb vaincre (to defeat or vanquish).

Could I say à cinq minutes instead?

Not for this meaning. À is used for a specific time on the clock (like à cinq heures for 'at five o'clock') or to describe physical distance (à cinq minutes d'ici means 'five minutes away'). To say something will happen in a certain amount of time from now, always use dans.