When OpenGL 4.1 was exposed in R600g for the select cards, I ran several benchmarks from my Radeon HD 6950 Cayman. I didn't have the chance to run any GL 4.1 tests with the Radeon HD 5830 Cypress since it was lodged away in a 4U system racked up for daily benchmarking. However, in cleaning and organizing some of the system racks this weekend, I pulled out the Radeon HD 5830 for running some tests.
The HD 5830 and other open-source AMD OpenGL 4.1-supporting cards were tested with Linux 4.5 and Mesa 11.2-devel from the Padoka PPA on Ubuntu 15.10.
OpenGL 4.1 was indeed working for this AMD Cypress GPU!
The HD 5830 was on par with the other graphics processors for DiRT Showdown in being largely CPU bound.
The HD 5830 comes in at just under 30 FPS when running Metro Last Light Redux at 1080p.
While not using OpenGL 4, here's the Counter-Strike: Global Offensive results just for showing a greater comparison of these GPUs. You can further analyze the results or run your own comparison via this OpenBenchmarking.org result file. There are also more Linux OpenGL benchmark results via today's More AMDGPU & Radeon Benchmarks Of Linux 4.5 With Mesa 11.2 Git.