<jats:title>Abstract</jats:title><jats:p>The CAST-CAPP axion haloscope, operating at CERN inside the CAST dipole magnet, has searched for axions in the 19.74 <jats:italic>μ</jats:italic>eV to 22.47 <jats:italic>μ</jats:italic>eV mass range. The detection concept follows the Sikivie haloscope principle, where Dark Matter axions convert into photons within a resonator immersed in a magnetic field. The CAST-CAPP resonator is an array of four individual rectangular cavities inserted in a strong dipole magnet, phase-matched to maximize the detection sensitivity. Here we report on the data acquired for 4124 h from 2019 to 2021. Each cavity is equipped with a fast frequency tuning mechanism of 10 MHz/ min between 4.774 GHz and 5.434 GHz. In the present work, we exclude axion-photon couplings for virialized galactic axions down to <jats:italic>g</jats:italic><jats:sub><jats:italic>a</jats:italic><jats:italic>γ</jats:italic><jats:italic>γ</jats:italic></jats:sub> = 8 × 10<jats:sup>−14</jats:sup> GeV<jats:sup>−1</jats:sup> at the 90% confidence level. The here implemented phase-matching technique also allows for future large-scale upgrades.</jats:p>