  In this paper, we establish several $q$-supercongruences modulo the fifth and
sixth powers of a cyclotomic polynomial in terms of several summation and
transformation formulas for basic hypergeometric series, the creative
microscoping method recently introduced by Guo and Zudilin, and the Chinese
remainder theorem for coprime polynomials. More concretely, we give a
$q$-supercongruence related to Van Hamme's (A.2) conjecture, a $q$-analogue of
a nice formula due to Long and Ramakrishna [Adv. Math. 290 (2016), 773--808],
and some $q$-supercongruences involving double series.
