  We notice that the famous pentagon identity for quantum dilogarithm functions
and the five-term relation for certain operators related to Macdonald
polynomials discovered by Garsia and Mellit can both be understood as specific
cases of a general "master pentagon identity" for group-like elements in the
Ding-Iohara-Miki (or quantum toroidal, or elliptic Hall) algebra. We perform
some checks of this remarkable identity and discuss its implications.
