Amd/ati was usually first to dump their old cards.
But now they're still selling gcn 1.0, so that's not happened yet.
HD 4000 and 5000 series were supposedly similar, yet had enough differences for AMD to move HD 4000 to Legacy already in 2012.
Once AMD revises its GCN architecture "enough", whether it'll be with Polaris or its successor, GCN 1.x might be put to Legacy
Last driver for HD 5000 and 6000 was Legacy Crimson Beta, though those cards don't seem to have gotten any performance drivers since GCN was released.
Based on AMD's history with driver support, I just don't dare to bet on more than 5-6 years, Legacy support year included, driver support for GCN 1.x
Has anyone seen benchmarks including Fermi and HD 5000-6000 series for DOOM? It's just OpenGL 4.3 so the game should at least start on those series