Pounding pounding pounding....

Above my head. Ready for today's Brain Bender via the handy dandy discount MENSA calendar??

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Harry was selling his baseball cards. The first buyer bought half; the second buyer bought one-forth of what was left, plus 5; the third buyer too half of what was left, plus 5; and the fourth and last buyer took half of what was left, plus 5. Harry held on to his 10 best cards.

How many cards did Harry start out with?

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Alrighty then, you know what to do. The answers will be found later in the comments. Happy Hump Day!