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Answer: 10 ways

Two 5ps: 5p + 5p

One 5p:  5p + 2p + 2p + 1p
               5p + 2p + 1p + 1p + 1p
               5p + 1p + 1p + 1p + 1p + 1p

No 5ps:   2p + 2p + 2p + 2p + 2p
               2p + 2p + 2p + 2p + 1p + 1p
               2p + 2p + 2p + 1p + 1p + 1p + 1p
               2p + 2p + 1p + 1p+ 1p + 1p + 1p + 1p
               2p + 1p + 1p+ 1p + 1p + 1p + 1p + 1p + 1p
               1p + 1p+ 1p + 1p + 1p + 1p + 1p + 1p + 1p + 1p

Total 10 ways




This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.