Aims. Coronal lines (CLs) may be a reliable proxy of supermassive black hole (SMBH) mass in active galactic nuclei (AGNs) because the production of these high ionisation potential (IP) lines is sensitive to the shape of the ionising continuum, which for a thin accretion disc relies on the black hole mass. In this work we study the connection between the [Ne V] CLs and the SMBH mass. Methods. We analysed the Spitzer spectra of a sample of 27 AGNs spanning three orders of magnitude in SMBH mass. Fluxes and the electron density in the coronal gas medium were measured after fitting Gaussians to both the [Nev]14µm and [Nev]24µm lines, where they were detected with a high signal to noise ratio. Results. Line fluxes were normalised to the Brγbroad emission from the broad-line region. We found strong correlations between the [Nev]14µm/Brγbroad and [Nev]24µm/Brγbroad line ratios and the SMBH mass. For this sample of 27 AGNs, we found scatters of 0.54 and 0.53 dex, respectively. These correlations support the theory that the coronal gas excitation is sensitive to a range of SMBH masses because of the dependence on the shape of the ionising continuum. The electron densities of the coronal medium are of the order of 1000cm-3, supporting their nuclear origin. A comparison with density values derived from JWST for a subsample of objects confirm this conclusion. Conclusions. These results further demonstrate the ability of CLs to be used as an SMBH mass proxy to allow for accurate SMBH mass measurements in AGNs.