As far as I know, the answer is no. The spirits under the Elemental Kings, can be likened to the legions under the Demonic Kings, in that they are infinite in number. The sylphs (Air), salamanders (Fire), gnomes (Earth) and undines (water). all possess the traits and qualities of their element. Konstantinos, in his book Summoning Spirits, gives brief descriptions of them, such as “the undines are very beautiful and staring too long at them can lead to obsession.”
As for the fifth element in the Persian system (the system of four elements plus ether or spirit is Persian in origin) it is usually seen as the guiding hand behind the elemental forces of the physical universe and therefore does not have spirits that embody it, beyond the Eternal Source which is behind everything. In the Chinese system of elements, they do not include Ether or Spirit, but have Wood, Air, Water, Fire, and Metal.