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Лучше поехать, ведь машину нужно доставить на мойку. Пройти 50 метров пешком можно, но без автомобиля это не имеет смысла.

Но до этого долго рассуждал:

We need to answer: "Автомойка находится в 50 метрах от моего дома. Мне нужно помыть машину. Пойти туда пешком или поехать?" This is a practical question: car wash is 50 meters from home. Should I walk or drive? The answer likely considers convenience, practicality, and perhaps humor. Since it's 50 meters, walking is trivial, but the car needs washing, so you need to bring the car to the car wash. So you should drive because you can't wash the car by walking. However, maybe it's a self-service car wash? But the question says "помыть машину" - to wash the car, and the car wash is nearby. Typically you drive your car to the car wash. So answer: you should drive, because you need the car there. But if it's only 50 meters, you could also walk and then drive? That doesn't make sense. So answer: поехать (drive). But the question may be a trick: it's so close, why drive? But you need the car there to wash it. So definitely drive. However, you might also consider if it's a manual car wash where you bring your own bucket? Probably not. So answer: поехать. Also, if it's 50 meters, walking is quicker than starting the car, etc. But the car is at home? So you need to move the car. So you should drive. I'll provide a concise answer in Russian.