Final answer:
The correct preposition to complete the sentence is 'in', as in 'I am going home in five days', which indicates a future action after five days.
Step-by-step explanation:
The student is asking for the correct preposition to fill in the blank in the sentence "I am going home ______ five days." The appropriate preposition to complete this sentence is "in," so the complete sentence should read "I am going home in five days." The use of "in" indicates that the action of going home will occur after the passing of five days.