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$q$-Supercongruences modulo the fifth and sixth powers of a cyclotomicpolynomial are very rare in the literature. In this paper, we establish some$q$-supercongruences modulo the fifth and sixth powers of a cyclotomicpolynomial in terms of Jackson's $_8\phi_7$ summation, Watson's $_8\phi_7$transformation, the creative microscoping method recently introduced by Guo andZudilin, and the Chinese remainder theorem for coprime polynomials. Moreconcretely, we give a $q$-analogue of a nice formula due to Long andRamakrishna [Adv. Math. 290 (2016), 773--808] and two $q$-supercongruencesinvolving double series.

$q$-Supercongruences from Jackson's $_8\phi_7$ summation and Watson's $_8\phi_7$ transformation