We both said the syllables go:
1) 5
2) 7
5) 5
We just said it differently.
Yes, Gary's initial explanation is correct.
People should bear in mind that the format of haiku is based on the Japanese language. This is an example of 5-7-5-syllable format (in fact, this is one of the best-known haiku by Basho Matsuo):
Furuike ya (5)
Kawazu Tobikomu (7)
Mizu no oto (5)
Meaning (according to my translation):
I see an old pond
Into which a frog jumps
Leaving the sound from the water
With the exceptsion of "n", every Japanese syllable consists of either the combination of one consonant and one vowel in this order, or one vowel. The "n" is not a vowel, but is counted as a syllable.
Haiku is the shortest and simplest form of Japanese poetry, and its trick is how much information and feeling the poet can put into each word in order to create the deepest and widest possible world and sensitivity to convey.
Interestingly and brilliantly, Gary pointed out that the lines of haiku rarely rhyme. That is probably because of the characteristics of the Japanese language and its words. Around 60 years ago, some of the most progressive Japanese poets tried to create Japanese poems according to the English sonnet format where the rhyming plays a significant role. But it turned out to be just impractical, and they found that the Japanese language was not made for that.