We investigate the conformal bootstrap approach to $O(N)$ symmetric CFTs in
five dimension with particular emphasis on the lower bound on the current
central charge. The bound has a local minimum for all $N>1$, and in the large
$N$ limit we propose that the minimum is saturated by the critical $O(N)$
vector model at the UV fixed point, the existence of which has been recently
argued by Fei, Giombi, and Klebanov. The location of the minimum is generically
different from the minimum of the lower bound of the energy-momentum tensor
central charge when it exists for smaller $N$.
To better understand the situation, we examine the lower bounds of the
current central charge of $O(N)$ symmetric CFTs in three dimension to compare.
We find the similar agreement in the large $N$ limit but the discrepancy for
smaller $N$ with the other sectors of the conformal bootstrap.