We study the performance of GaN nanowire n-MOSFETs (GaN-NW-nFETs) with a channel length, Lg = 5 nm based on fully ballistic quantum transport simulations. Our simulation results show high I ${} _{\textsf {ON}} = 1137 \mu \text{A}/\mu \text{m}$ and excellent on-off characteristics with Q $ = \,\, \text{g}_{\textsf {m}}$ /SS $ = \,\, 188\mu \text{S}$ -decade/ $\mu \text{m}$ -mV calculated for I ${} _{\mathrm{\scriptscriptstyle OFF}} = 1$ nA/ $\mu \text{m}$ and V ${} _{\textsf {GS}} = \textsf {V}_{\textsf {DS}} = \textsf {V}_{\textsf {CC}} = 0.5$ V. These results represent: 1) ~ 15% higher $\text{I}_{\mathrm{\scriptscriptstyle ON}}$ than Si-NW-nFET and 2) ~ 17% better Q than Si-NW-nFET, all with Lg = 5 nm, thus suggesting the GaN n-channel, an intriguing option for application in logic at sub-10-nm channel length. The superior performance of the GaN channel compared with Si and other semiconductors at this scaled dimension can be attributed to its relatively higher effective mass of electron and lower permittivity.