  The thermodynamics of d5 AdS BHs with positive, negative or zero curvature
spatial section in higher derivative (HD) gravity is described. HD contribution
to free energy may change its sign which leads to more complicated regime for
Hawking-Page phase transitions. Some variant of d5 HD gravity is dual to ${\cal
N}=2$ $Sp(N)$ SCFT up to the next-to-leading order in large $N$. Then,
according to Witten interpretation the stable AdS BH phase corresponds to
deconfinement while global AdS phase corresponds to confinement. Unlike to
Einstein gravity in HD theory the critical $N$ appears. It may influence the
phase transition structure. In particulary, what was confining phase above the
critical value becomes the deconfining phase below it and vice-versa.
