In MQMAS-based high-resolution solid-state NMR experiments of half-integer spin quadrupolar nuclei, the high radiofrequency (RF) field requirement for the MQ excitation and conversion steps with two hard-pulses is often a sensitivity limiting factor in many practical applications. Recently, the use of two cosine-modulated (cos) low-power (lp) pulses, lasting one-rotor period each, was successfully introduced for efficient MQ excitation and conversion of spin-3/2 nuclei with a reduced RF amplitude. In this study, we extend our previous investigations of spin-3/2 nuclei to systems with higher spin values and discuss the applicability of coslp-MQ excitation and conversion in MQMAS and MQ-HETCOR experiments under slow and fast spinning conditions. For the numerical simulations and experiments we used a moderate magnetic field of 14.1 T. Two spin-5/2 nuclei (85Rb and 27Al) are mainly employed with a large variety of CQ values, but we show that the practical set up is also available for higher spin values, such as spin-9/2 with 93Nb in Cs4Nb11O30. We demonstrate for nuclei with spin value larger than 3/2 a preferential use of coslp-MQ acquisition for low-gamma nuclei and/or large CQ values with a much reduced RF-field with respect to that of hard-pulses used with conventional methods.