  With the discovery of some hidden-charm pentaquark resonances by the LHCb
Collaboration, investigations of pentaquark states containing heavy quarks have
aroused the interest of theorists. We study herein $qqq\bar{q}Q$ ($q = u$ or
$d$, $Q=c$ or $b$) pentaquark system, in the framework of the chiral quark
model. In consequence, some charmed and bottomed pentaquarks are considered to
exist by five-body dynamical calculations. In the charm sector,
$\Sigma_c\pi(IJ^P=0\frac{1}{2}^-)$ and $\Sigma_c^*\pi(IJ^P=0\frac{3}{2}^-)$ are
possible candidates of $\Lambda_c(2595)$ and $\Lambda_c(2625)$, respectively.
Besides, two high-spin states, $\Sigma_c^*\rho(IJ^P=0\frac{5}{2}^-)$ and
$\Delta D^*(IJ^P=1\frac{5}{2}^-)$, are also found in the energy region of $3.2
\sim 3.3$ GeV. In the bottom sector, $\Sigma_b\pi(IJ^P=0\frac{1}{2}^-)$,
$\Sigma_b^*\pi(IJ^P=0\frac{3}{2}^-)$ could be candidates of $\Lambda_b(5912)$
and $\Lambda_b(5920)$, respectively. And $\Sigma_b^*\rho(IJ^P=0\frac{5}{2}^-)$
and $\Delta B^*(IJ^P=1\frac{5}{2}^-)$ are found in the energy region of $6.5
\sim 6.6$ GeV. $\Sigma_c^{(*)}\pi$ and $\Sigma_b^{(*)}\pi$ are expected as
compact states, while $\Sigma_c^*\rho$, $\Sigma_b^*\rho$, $\Delta D^*$ and
$\Delta B^*$ are expected as molecular states.
