So I decided to do a post on different 5 line poetry forms I could remember knowing or reading about :
Gogyohka : Gogyohka is five lines of free verse on any subject matter. There is no set syllable pattern, however the poem should be short and succinct. The goal is to compellingly capture an idea, observation, feeling, memory, or experience in just a few words.
Along this i also found a mention of Gogyoshi which also is a 5 line poem.
Fib : is an experimental Western poetry form, but based on the Fibonacci sequence (1/1/2/3/5/8) Traditionally that started with 6 -lines, now can be written in as many lines. The only restriction is to use the mentioned sequence as syllable count in each line.
Cinquain : A general term for 5 line poems with a set pattern.Either word count / syllable count of 2-4-6-8-2 is most commonly known. There is another pattern used for ease of expression : noun – 2 adjectives – 3 ing words – a phrase – synonym of noun [ this is also referred to as didactic cinquain]
Limerick : are usually humorous, and are composed of 5 lines, in an a. a. c. c. a. rhyming pattern. In addition, the first, second and fifth lines are usually 3 anapestic feet (uu/, 2 unstressed followed by 1 stressed) each.
Tanka : is a japanese form of poetry with syllable patterns as 5-7-5-7-7 , where the care is to be taken that both the first three and the last three lines can stand on its own and make a sensible poetry. (More details here)
Lanterne : 5 – line poetry in shape of japanese lantern and having syllable count as 1-2-3-4-1 , each line able to stand on its own with or without a title. (Wiki link)
CINQKU : (As detailed here)is a fixed-form five line tanka/cinquain image poem without a title in 17 syllables,concise with a surprise or turn in lines 4/5
ABC poem : has 5 lines that create a mood, picture, or feeling. Lines 1 through 4 are made up of words, phrases or clauses – and the first word of each line is in alphabetical order from the first word. Line 5 is one sentence, beginning with any letter.
Another version says that ABC poem can have any number of line but the restriction with that the lines start with Alphabets in order.
Envelop Quintet : Rhyme pattern of abbba / abcba ( Details here )