Some types of compact fluorescent (PLL, PLT) have a push-in fitting. Try pulling straight out.

[![enter image description here][1]][1]

I'd try undoing a similar bulb in a similar nearby fitting to verify that the fitting is a normal Edison screw (unless you are in the UK, where you might have a bayonet fitting that needs to be pushed in 2 mm then turned 90° widdershins). 

P.S. While you are working on that, you really ought to fix that loose earth/ground connection with a bolt, nut, washer and maybe a crimp-on ring-connector. Or something similar. —

P.P.S. broken compact fluorescents [may need special cleanup](https://www.epa.gov/cfl/cleaning-broken-cfl)


  [1]: https://i.sstatic.net/PGoA9.png