Learn French: Le spectacle va commencer dans cinq minutes. - The show is going to start in five minutes.

It does mean "inside" for physical locations, but for time, dans is the word you use to mean "in an amount of time from now". It is the standard way to say when a future event will happen, like dans cinq minutes.

Could I use en instead of dans to say "in five minutes"?

No, and this is a classic trap! You must use dans to say when an event will happen in the future. You use en to say how long it takes to complete an action (for example, "I finished the test en cinq minutes").

Why use va commencer instead of a regular future tense?

Va commencer is the near future tense, made with the verb aller (to go) plus the infinitive commencer (to start). It translates exactly to "is going to start". It is the most natural choice here because the event is happening very soon.

Does spectacle mean a crazy scene, like a "spectacle" in English?

It can, but much more often un spectacle is simply the everyday French word for a live entertainment show, a play, a performance, or a concert.