The term for a linked-verse poem with alternating 5-7-5 and 7-7 stanzas is renga. The name means “linked poem,” describing a sequence in which poets connect their verses one after another.
Renga developed from earlier Japanese verse exchanges and became a highly regulated collaborative art during the medieval period. A typical long sequence alternated short 5-7-5 stanzas with 7-7 stanzas, measured in Japanese morae rather than exactly the same syllable counts used in English. Renga sessions were often composed aloud at gatherings and later transcribed.
The opening 5-7-5 stanza was called the hokku. It was expected to establish the season and setting, often using a kigo, or seasonal word. The hokku eventually became an independent poetic form: what is now called haiku. Renga also helped produce haikai and related linked-verse forms.
A common mix-up is waka, which usually refers to a self-contained 5-7-5-7-7 poem, especially the tanka form. Renga is collaborative and sequential, while waka is normally a complete individual poem.