  A five dimensional braneworld cosmological model in general scalar-tensor
action comprises of various Horndeski Lagrangian is considered. The Friedmann
equations in the case of the strongly and weakly coupled $\mathcal{L}_5$
Horndeski Lagrangian have been obtained. The strongly coupled $\mathcal{L}_5$
model produces the Cardassian term $\rho^n$ with $n=\pm 1/2$, which can served
as alternative explanation for the accelerated expansion phase of the universe.
Furthermore, the latest combined observational facts from BAO, CMB, SNIa,
$f_{\sigma_8}$, and $H_0$ value observation suggest that the $n=-1/2$ term lies
quite close to the constrained value. On the other hand, the weakly coupled
$\mathcal{L}_5$ case has several new correction terms which are omitted in the
braneworld Einstein-Hilbert model, e.g. the cubic $\rho^3$ and the dark
radiation-matter interaction term $ \chi a^{-4}\rho$. Furthermore, this model
provides a cosmological constant constructed from the bulk scalar field,
requires no brane tension, and supports the big bang nucleosynthesis (BBN)
constraint naturally.
