In this paper, a (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada system is investigated in fluid mechanics via the symbolic computation. With the help of the Hirota method, we derive the singular soliton, shock-wave, breather-stripe soliton and hybrid solutions. Based on the finite difference method, we get the numerical one-soliton solutions. We graphically show the singular and shock-wave solutions, and observe that the singular one-soliton solutions are blow-up and unstable, but the shock-wave solutions are nonsingular and stable. We observe that the breather-stripe soliton moves along the negative direction of the y axis, where y is a variable, and the amplitude and shape of the breather-stripe soliton remain invariant during the propagation. We graphically demonstrate the interaction among a rogue wave, a periodic wave and a pair of stripe solitons: a rogue wave arises from one stripe soliton; the rogue wave interacts with the periodic wave, the rogue wave splits into two waves and then the two waves merge into a wave; the rogue wave fuses with the other stripe soliton. We graphically present that the numerical solutions are well approximate to the analytic solutions.