Security and access control for data storage in 5G industrial Internet collaborative systems are facing significant challenges. The characteristics of 5G networks, such as low latency and high speed, facilitate data transmission in the industrial Internet but also increase vulnerability to attacks like theft and tampering. Moreover, in 5G industrial Internet collaborative system environments, data flows across multiple entities and links, which necessitates a flexible access control model to meet specific data access requirements. Traditional role-based and attribute-based access control mechanisms are difficult to apply in such dynamic application scenarios. To address these challenges, we propose a novel data storage solution for 5G industrial Internet collaborative systems. Similar to existing approaches, it provides integrity and confidentiality protection for transmitted data. In terms of security, only authenticated data owners and users can obtain file decryption keys, preventing malicious attackers from data forgery. Regarding access control, decryption is permitted only to authorized data users, safeguarding against unauthorized file access. Furthermore, by introducing an attribute-based encryption mechanism, only data users with specific attributes can decrypt files. In terms of efficiency, our approach utilizes bilinear and modular exponentiation operations solely during the authentication process. For handling substantial data loads, lightweight cryptographic algorithms are employed. Consequently, our solution achieves higher efficiency compared with other known methods. Experimental results demonstrate the feasibility of our approach in real-world applications.