"participatory" into its individual syllables:
par-tic-i-pa-tory
A syllable is a unit of sound in a word that contains a vowel sound. In this case:
"par" is one syllable
"tic" is one syllable
"i" is one syllable
"pa" is one syllable
"tory" is one syllable
Therefore, the word "participatory" has a total of 5 syllables.