Snake on street? Exaggerated statement maybe (5)
I believe the answer is:
boast
'exaggerated statement maybe' is the definition.
(a boast is an exaggerated claim)
'snake on street?' is the wordplay.
'snake' becomes 'boa' (boa is a kind of snake).
'on' means one lot of letters go next to another.
'street?' becomes 'st' (abbreviation).
'boa'+'st'='BOAST'
(Other definitions for boast that I've seen before include "Talk with excessive pride" , "Blow one's own trumpet" , "Expression of excessive pride" , "Talk conceitedly" , "Talk big" .)