Nope. Draw it out. He will still be 5 miles from his house wherever he starts
English
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You understand he isnt going straight for five miles, taking a right and going five miles and then taking another right and going five miles. The northernmost point you can get to is the north pole If you start at the north pole and go south Then go west Then go north You end up at the north pole again. You might be facing a different direction But you always will end up at the north pole again.
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If he goes straight 5 miles, then right 5 miles, the walk back to his house won't be 5 miles