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The Kennicutt-Schmidt (KS) relation between the gas and the star formation rate (SFR) surface density ($\Sigma_{\rm gas}$-$\Sigma_{\rm SFR}$) is essential to understand star formation processes in galaxies. So far, it has been measured up to z~2.5 in main-sequence galaxies. In this letter, we aim to put constraints at z~4.5 using a sample of four massive main-sequence galaxies observed by ALMA at high resolution. We obtained ~0.3"-resolution [CII] and continuum maps of our objects, which we then converted into gas and obscured SFR surface density maps. In addition, we produced unobscured SFR surface density maps by convolving Hubble ancillary data in the rest-frame UV. We then derived the average $\Sigma_{\rm SFR}$ in various $\Sigma_{\rm gas}$ bins, and estimated the uncertainties using a Monte Carlo sampling. Our galaxy sample follows the KS relation measured in main-sequence galaxies at lower redshift and is slightly lower than predictions from simulations. Our data points probe the high end both in terms of $\Sigma_{\rm gas}$ and $\Sigma_{\rm gas}$, and gas depletion timescales (285-843 Myr) remain similar to z~2 objects. However, three of our objects are clearly morphologically disturbed, and we could have expected shorter gas depletion timescales (~100 Myr) similar to merger-driven starbursts at lower redshifts. This suggests that the mechanisms triggering starbursts at high redshift may be different than in the low- and intermediate-z Universe., Comment: 9 pages, 7 figures, 2 tables, accepted by A&A (letter)