There are a lot of companies that see the value in someone who loves writing code and solving problems. If I asked that question (which I wouldn't, I hate it) I would be happy to hear the following as an answer:

"I love coding, so I hope that whatever I'm doing in five years, I'll still have my hands dirty solving real problems. I also love learning and sharing my knowledge with others. While I'm not interested in being a technical manager, I would like to be a technical leader."