  d5 higher derivative gravity on the Schwarzschild-de Sitter (SdS) black hole
background is considered. Two horizons SdS BHs are not in thermal equilibrium
and Hawking-Page phase transitions are not expected there, unlike to the case
of AdS BHs. It is demonstrated that there exists the regime of d5 theory where
Nariai BH which is extremal limit of SdS BH is stable. It is in the contrast
with Einstein gravity on such backgroundwhere only pure de Sitter space is
always stable. Speculating on the applications in proposed dS/CFT
correspondence, these two (de Sitter and Nariai) stable spaces may correspond
to confining-deconfining phases in dual CFT.
