There is no canonical x^5 formula for warp drives in Star Trek.
Between the Original Series/Kirk era and the Next Generation/Picard era they changed the scale, never explained why, and the real reason is that Gene Roddenberry wanted Warp 1 to be the speed of light, Warp 10 to be infinite, and Warp 6 to be a good cruising speed that gets you from planet to planet fast enough for a normal Trek episode, so they came up with a completely arbitrary chart that's been in every official Star Trek product on the material for the last 15 years; the Next Generation Technical Manual, Star Trek Encyclopedia, and all the Last Unicorn Games versions of Trek (which had much more official oversight in their production than the FASA materials). The Next Generation technical manual and Encyclopedia gloss over the issue, implying that further research into warp sciences revealed that this is the "real" scale and what came before was a less perfect understanding of warp.
The x^3 formula was used in the original series (and now Enterprise) era, for warp drive. There is virtually no dispute on that fact (and among my fairly expansive Star Trek reference library I do have a copy of the FASA Next Generation book with the questionable formula in it).
When FASA wrote it's Next Generation Officer's Manual, it was right after the 1st Season of Next Generation, when there was a dearth of official information being handed out, and from the looks of things FASA had no real access to Trek production offices or inside information, and made up whatever they wanted that fit with their existing source material and the series "bible", so they came up with their own independent explanation of all the various little things left unspoken, like what the new warp scale meant (it was the "Ultra Warp" system that was supposed to be faster than Transwarp). The problem is, that FASA made up an awful lot of stuff whole-cloth that was utterly ignored by Paramount in later years. Star Trek has never been extremely sharp with continuity of licensed materials, and the FASA RPG was a textbook case of that.
Anything from the FASA Star Trek game is highly suspect, and definitely not authoritative reference material. The infamous Star Trek: Next Generation Officer's Manual which had the x^5 formula for Next Generation is widely believed to be part of the reason that FASA lost the Trek license, it was a train-wreck of a book that made wide, sweeping assumptions about the Next Generation era and virtually all of them have been proven wrong (FASA's stardate system, Transwarp drives being perfected and standard in Starfleet, the saucer section of a Galaxy Class Starship being capiable of independent warp flight, and their profile views of starships are so blatantly wrong it's almost comical when you realize they don't look like what they are shown as on screen: Constellation Class ships and Romulan Warbirds look all wrong among other things).
If you really want exact page quotations and citations, I can provide them, but I won't bother unless people really want them.