Yes, you CAN use crimson with the 5000 series:
https://community.amd.com/docs/DOC-1435
AMD Radeon™ Software Support for Legacy Graphics Products
AMD Radeon Software Crimson Edition Beta Driver
Applicable Products:
•AMD Radeon™ HD 7000 – HD 7600 (including A/D/G variants) Series Graphics
•AMD Radeon™ HD 6000 (including A/D/G/M variants) Series Graphics
•AMD Radeon™ HD 5000 (including M variant) Series Graphics