The drone's open and untrusted environment may create problems for authentication and data sharing. To address this issue, we propose a blockchain-enabled efficient and secure data-sharing model for 5G flying drones. In this model, blockchain and attribute-based encryption (ABE) are applied to ensure the security of instruction issues and data sharing. The authentication mechanism in the model employs a smart contract for authentication and access control, public-key cryptography for providing accounts and ensuring accounts security, and a distributed ledger for security audit. In addition, to speed up outsourced computations and reduce electricity consumption, an ABE model with parallel outsourced computation (ABEM-POC) is constructed, and a generic parallel computation method for ABE is proposed. The analysis of the experimental results shows that parallel computation significantly improves the speed of outsourced encryption and decryption compared with serial computation.