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Due to the coexistence of many emergent phenomena, including 2D superconductivity and a large Rashba spin-orbit coupling, 5d transition metal oxides based two-dimensional electron systems (2DESs) have been prospected as one of the potential intrants for modern electronics. However, despite the lighter electron mass, the mobility of carriers, a key requisite for high-performance devices, in 5d-oxides devices remains far behind their 3d-oxides analogs. The carriers mobility in these oxides is significantly hampered by the inevitable presence of defects generated during the growth process. Here, we report very high mobility ($\sim$ 22650 cm$^2$V$^{-1}$s$^{-1}$) of 5d-2DES confined at the LaAlO$_3$/KTaO$_3$ interface. The high mobility, which is beyond the values observed in LaAlO$_3$/SrTiO$_3$ and $γ$-Al$_2$O$_3$/SrTiO$_3$ systems in the same carrier-density range, is achieved using the ionic-liquid gating at room temperature. We postulate that the ionic-liquid gating affects the oxygen vacancies and efficiently reduces any disorder at the interface. Investigating density and mobility in a broad range of back-gate voltage, we reveal that the mobility follows the power-law $μ\propto n^{1.2}$, indicating the very high quality of ionic-liquid-gated LaAlO$_3$/KTaO$_3$ devices, consistent with our postulate. Further, the analysis of the quantum oscillations measured in high magnetic fields confirms that the high-mobility electrons occupy the electronic sub-bands emerging from the Ta:5d orbitals of KTaO$_3$.