N5
どうして
Why
どうしてここにいるの？
Why are you here?
Explanation
「どうして」 means 'why' and is the most basic, natural way to ask for a reason; it works in polite everyday conversation and in ordinary writing. It often carries a feeling of 'I don't get it', 'what a surprise' or 'I'm worried': 「どうして知っているの？」 (How come you know?), 「どうして来なかったんですか？」 (Why didn't you come?).
Mixed up with
「どうして」 is warmer than 「なぜ」. When a friend looks down, 「どうしてそんなに元気がないの？」 (Why are you so down?) sounds caring; with 「なぜ」 it would sound like a police statement. In scientific papers and legal documents, though, use 「なぜ」 rather than the emotional 「どうして」.