We report on the discovery of five carbon-enhanced metal-poor (CEMP) stars in the metallicity range of -3.3<[Fe/H]{<}-2.4. These stars were selected from the LAMOST DR3 low-resolution (R~2000) spectroscopic database as metal-poor candidates and followed up with high-resolution spectroscopy (R~110000) with the Lick/APF. Stellar parameters and individual abundances for 25 chemical elements (from Li to Eu) are presented for the first time. These stars exhibit chemical abundance patterns that are similar to those reported in other literature studies of very and extremely metal-poor stars. One of our targets, J2114-0616, shows high enhancement in carbon ([C/Fe]=1.37), nitrogen ([N/Fe]=1.88), barium ([Ba/Fe]=1.00), and europium ([Eu/Fe]=0.84). Such chemical abundance pattern suggests that J2114-0616 can be classified as CEMP-r/s star. In addition, the star J1054+0528 can be classified as a CEMP-rI star, with [Eu/Fe]=0.44 and [Ba/Fe]=-0.52. The other stars in our sample show no enhancements in neutron-capture elements and can be classified as CEMP-no stars. We also performed a kinematic and dynamical analysis of the sample stars based on Gaia DR2 data. The kinematic parameters, orbits, and binding energy of these stars show that J2114-0616 is member of the outer-halo population, while the remaining stars belong to the inner-halo population but with an accreted origin. Collectively, these results add important constraints on the origin and evolution of CEMP stars as well as on their possible formation scenarios.