The kata we refer to as Gojushiho-Dai is also refered to as Gojushiho-Sho. They are two kata which follow eachothers pattern very closely.
It is not widely known that the two kata have had their names reversed by the JKA. The SKI still sticks to the original naming, which we follow as well. However, Gojushiho-Sho is not part of our syllabus.
Originally, Gojushiho Dai was the name given to the more basic of the two. (the one we refer to here!)
Containing many back stances and larger scale movements than the original Sho kata, this is the one believed to have been created first and the Sho kata was thought to be added later. However, it is rumoured that in a JKA tournament some years ago, a now very high-ranking Ueki performed the Dai kata while accidentally calling out the name "Gojushiho-Sho!" in the last round of competition on National Television in Japan.
According to this story, the judges were befuddled, since the performance was perfect, about what to do with Ueki and his misnamed kata. Their solution: give Ueki first place, and switch the names of the two kata. So, today the karateka who outrank Ueki generally call the more basic kata Dai. However, most people in the JKA, and the Best Karate series of books refer to the more difficult kata as Dai and the easier kata as Sho. Is the story about Ueki true? Maybe not.
There is a little evidence to support it. Kanazawa, in his books, names the kata Dai and Sho in the reverse from their names in Best Karate by Nakayama. Kanazawa was a student of Nakayama's, but also much more prestigious a man in the JKA than Ueki. Did Kanazawa reject the renaming of the kata in favour of their proper names? Maybe... Kanazawa did quit the JKA to form the SKI which still uses the original naming.
If the names of the Gojushiho kata were reversed for this reason, and if the story is true, then that means that everyone in the JKA style of Shotokan learns the names reversed because a 40 year old man wanted a plastic trophy with 1st Place written on it.

We also practise the older version of this kata which is just called Gojushiho or Oueshi and which supposedly finds its roots in Drunken Style Boxing.