"Do you like sports?"
Japanese grammar is different from English grammar. No language will have the same grammar or order of placement. When studying another language, after the phrase or sentence has been translated, you need to change the order or add a few words to make it valid in the language it is being translated to.
That's a totally understandable misconception. は and が would both make sense with 好き, but the meaning is different; I can't really explain it well, since I'm an amateur myself, but:
は is the "topic" particle, and が is the "subject" particle. So, my take on that is, if you're discussing sports in general, you'd say スポーツは好き, but if sports come up and you want to state your stance on them, you'd say スポーツが好き.
Another example; if someone asked you if you liked sports, you might reply: いいえ、 スポーツが好きじゃないですでもチェスは好きです。