Olympus introduced the E-M5 in 2012. (I bought one right away.) It was a major step up in image quality from all previous m43 cameras using the old 12MP sensor. At about the same time (just before in fact) Panasonic introduced the GX1, a camera never loved because of shutter shock.
Much after the E-M5 came the E-M10 (lower end, not weather sealed and IBIS not as good) and the E-M1 (higher end, with PDAF).
Since then the E-M5 got an update, the E-M10 and fairly recently the E-M1.
Olympus has its focus on photography, not video recording. The E-M10 got an update with 4K video in the mark III and the E-M1 got that update with the mark II. The E-M5 still does not have that update, but frankly, in terms of stills photography the E-M5 II is still a very good camera. What could we expect from an E-M5 III besides the insignificant increase in resolution from 16 to 20MP and the 4K video? Not much I believe, because the E-M5 II is already very good. Some people dream of PDAF but that is very unlikely to come to the E-M5 series as it is reserved for the E-M1 series. So there is no rush for an E-M5 III because there is only a small wishlist.