  In this paper, we explore the period tripling and period quintupling
renormalizations below $C^2$ class of unimodal maps. We show that for a given
proper scaling data there exists a renormalization fixed point on the space of
piece-wise affine maps which are infinitely renormalizable. Furthermore, we
show that this renormalization fixed point is extended to a $C^{1+Lip}$
unimodal map, considering the period tripling and period quintupling
combinatorics. Moreover, we show that there exists a continuum of fixed points
of renormalizations by considering a small variation on the scaling data.
Finally, this leads to the fact that the tripling and quintupling
renormalizations acting on the space of $C^{1+Lip}$ unimodal maps have
unbounded topological entropy.
