  This Letter reports on the first results from the Taiwan Axion Search
Experiment with Haloscope, a search for axions using a microwave cavity at
frequencies between 4.70750 and 4.79815 GHz. Apart from the non-axion signals,
no candidates with a significance more than 3.355 were found. The experiment
excludes models with the axion-two-photon coupling
$\left|g_{a\gamma\gamma}\right|\gtrsim 8.2\times 10^{-14}$ GeV$^{-1}$, a factor
of eleven above the benchmark KSVZ model, reaching a sensitivity three orders
of magnitude better than any existing limits in the mass range 19.4687 < $m_a$
< 19.8436 $\mu$eV. It is also the first time that a haloscope-type experiment
places constraints on $g_{a\gamma\gamma}$ in this mass region.
