Gan have released many excellent speedcubes but they have never ventured beyond the 4x4x4 and even when they did make a 4x4x4 it was met with significant criticism. So, no, there is no Gan 5x5x5 (or 6x6x6, 7x7x7...)

For many years Gan focused purely on 3x3x3 speedcubes but started to release some other puzzles around 2018, initially the Gan 249 which not many cubers liked, but Gan improved their 2x2x2 options and now their Gan 251 M Pro is used by many top 2x2 solvers. Gan also released a pyraminx in 2020 which has been moderately well received but most top cubers prefer a well set-up YuXin Little Magic or a Weilong. Shortly after the pyraminx, Gan released a skewb and their skewb is used almost universally among the top speedcubers and other skewbs have failed to compete.

Gan have made so many excellent products in the smaller events that they probably see no value in investing loads of time and money into developing larger cubes which may very easily flop like their 4x4x4 did, for this reason I do not expect Gan to release another 4x4x4 anytime soon and I certainly don't expect a 5x5x5, I could be wrong and if I am I am excited to try Gan's attempts at designing big cubes.