In order to support delay-bounded multimedia services over 5G mobile wireless networks, the statistical quality-of-service (QoS) technique has been designed to jointly guarantee statistically delay-bounded video transmissions over different time-varying wireless channels, simultaneously. In addition, with short transmission delay requirements for the multimedia data transmissions, the traditional Shannon's capacity is no longer appropriate to characterize the maximum achievable data transmission rate given the block error probability. Towards this end, the finite blocklength coding (FBC) technique has been developed for reliable delay-bounded 5G multimedia mobile wireless networks. Recent results have derived the throughput of FBC subject to statistical delay-bounded QoS constraints given the block error probability. However, it is challenging to characterize the effective capacity for multimedia data transmissions over fading channels while guaranteeing statistical delay-bounded QoS constraints in the finite blocklength regime. To effectively remedy the above-mentioned deficiencies, we propose FBC based cross-layer design while guaranteeing statistical delay-bounded QoS requirements over 5G multimedia mobile wireless networks. In particular, we establish and analyze FBC based wireless network models. Given statistical delay-bounded QoS constraints, we formulate and solve the e-effective-capacity optimization problem with FBC. Also conducted is a set of simulations which validate and evaluate our proposed FBC scheme under statistical delay-bounded QoS constraints.