In addition to their great astrophysical interest, quasars represent quasi-ideal reference objects in the celestial sphere with, a priori, a lack of significant proper motion. Since the fourth release of the Large Quasar Astrometric Catalogue (LQAC-4), a large number of quasars have been discovered, in particular those coming from the DR14Q release of the SDSS. With the advent of the Gaia Data Release 2 (DR2), it is now also possible to fold in extremely accurate quasar positions. Following the same procedure as in the previous releases of the LQAC, our aim is to compile the large majority of the recorded quasars, with their best estimated coordinates and substantial information about their physical properties such as the redshift, multi-bands apparent, and absolute magnitudes. Emphasis is given to the results of the cross-matches with the Gaia DR2 catalogue, which considerably increases the positional accuracy. New quasars from the SDSS DR14Q release were cross-matched with the precedent LQAC-4 compilation with a 1" search radius, which leads to 149084 objects not present in the previous LQAC-4 release. Another cross-match was done with the Gaia DR2 catalogue, which enables us to considerably improve the positioning of these objects. For the first time, parallaxes and proper motions from the DR2, when available, are added to our compilation. Furthermore, a cross-identification of the LQAC-5 with the AllWISE survey gives additional mid-infrared information for an important percentage of objects. Our final catalogue, namely the LQAC-5, contains 592 809 quasars. This represents roughly a 34% increase with respect to the number of objects recorded in the LQAC-4. Among them, 398 697 objects were found in common with the Gaia DR2, within a 1" search radius. That corresponds to 67.26% of the whole population of the compilation. The LQAC-5 delivers a nearly complete catalogue of spectroscopically confirmed quasars (including a small proportion of 14126 compact AGN's) to the astronomical community, with the aim of giving their best equatorial coordinates with respect to the ICRF2 and with exhaustive additional information. For more than 50% of the sample, these coordinates are extracted from the very recent Gaia DR2.