Je finis dans 5 minutes

Laura, 

it is common in French to use the present tense or the future proche for events in the very near or near future. The English translation could just as easily have said ' I am finishing in 5 minutes ' depending on the context. Note that French doesn't use ' être ' as part of the equivalent construction.

Often ' will do something ' in English is a good match to using future tense in French, but as here, that is not always the case. 

The future simple is not generally used for something this near in the future, especially not in everyday spoken French.

 

See the link below from here regarding the present tense and near future, and also the link below from Camille at French Today from which the following has been copied about practical difference between the future proche ( more commonly used in speech ) and the future simple tenses. 

                "In spoken French, the futur proche is commonly used to describe events expected to occur soon, emphasizing the speaker’s belief in the action’s imminence. The futur simple is often reserved for formal writing or to discuss events that are more distant or less certain " 

The article also includes some comments on present tense compared to future tense, pertinent to the example you have given.

Remember the translation is just the same or similar idea expressed in ' colloquial ' English, and tenses between the 2 languages do not always match.

 Expressing immediate and near-future actions with the present tense (Le Présent) in French

 https://www.frenchtoday.com/blog/french-verb-conjugation/2-french-future-tenses-futur-proche-simple/