To upper-bound both delay and error-rate for sup-porting time-sensitive multimedia services over 5G and beyond (5G+) mobile wireless networks, researchers have developed several advanced techniques, including statistical delay-bounded quality-of-service (QoS) provisioning and finite blocklength coding (FBC). On the other hand, cell-free massive-multi-input multi-output (m-MIMO) system, where a large number of distributed access points (APs) jointly serve all users in a coordinated manner, has emerged as one of the key promising techniques to significantly improve various mobile QoS performance indices, including throughput, user-coverage probability, energy/spectrum efficiencies, etc. Inspired by the more diverse distances between mobile users and APs in cell-free m-MIMO systems compared with traditional centralized m-MIMO systems, integrating non-orthogonal multiple access (NOMA) with cell-free m-MIMO can significantly enhance spectral efficiency for massive connections of mobile devices. But, due to the complexity of analyzing the networking dynamics in the finite blocklength regime, how to efficiently characterize the queuing process for cell-free m-MIMO-NOMA schemes using FBC based statistical delay/error-rate bounded QoS theory is still an open problem. To solve the above challenges, we propose FBC based cell-free m-MIMO-NOMA schemes over 5G+ mobile wireless networks under statistical delay/error-rate bounded QoS constraints. In particular, we establish cell-free m-MIMO-NOMA system models over Rician wireless fading channels. Considering statistical delay/error-rate bounded QoS constraints, we derive a closed-form expression for an upper bound on the delay violation probability over downlink Rician wireless fading channels with non-vanishing error probability. Our simulation results validate and evaluate our proposed FBC based cell-free m-MIMO-NOMA schemes.