That is a really good question... so I asked google.
Evidently Solace did a song called Shoush in 5/8 Rhythm.
Bellydance.one has an article on "20 Middle Eastern Dance Rhythms Simplified" that references Shoush.
17. Shoush
5/8 Rhythm
1 2 3 1 2
D tk tk D T
D _ _ _ t _ k _ T _ _ _ D _ _ _ T _ _ _
According to the book "Dynamic Belly Dance, The Joyful Journey of Dancemaking and Performing Paperback – May 4, 2007 by Ramona" (p.110) Greek and Turkish BD music does include a 5/8 rhythm.
5-beat 5/4 and 5/8 rhythms are rare. 5-beat rhythms appear in Turkish and Greek music, Moroccan Jajuka trance dances, East Indian music, and American Jazz. The related 10/8 rhythm is prevalent in Armenian music & line dances.
There's a dancer, Debora Newberg, in Santa Fe New Mexico who teaches a workshop:
4) Dancing with Odd Rhythms ~ Have fun dancing with Odd Rhythms! Main focus will be on Turkish 9/8 and 7/8, and we’ll also visit the Arabic 10/8 (Samai), the Armenian 10/8, Persian and Moroccan 6/8s and even 11/8 and 5/8!
There is also someone named Tayyar Akdeniz who teaches music and does folk tours in Turkey who evidently does a workshop that covers 5/8 rhythms.
So basically it looks like if you want to know about 5/8 rhythms in BD you should probably ask dancers or musicians who specialize in Greek and Turkish styles.