You mean that your display is FHD (1920*1080) but there are only resolution
options up to 1280*1024 available in the operating system?
Try to connect the display to your graphics card (either discrete or
integrated) via digital interface (either DVI, HDMI or DP), then the
operating system should be able to detect the correct resolution.
I believe this is not very relevant to the graphics card. I once connected a
second-hand low-end LCD to Intel HD4000, and only resolutions up to 1024*768
were available under GNU/Linux, and the display had only VGA (analog)
interface. (But it worked perfectly under Losedows...)
However, if you have Intel integrated graphics, be sure to physically remove
this AMD HD5450. Intel graphics starting Sandy Bridge (2nd. gen. Core
processors) are way better than it. If you still want a discrete graphics
card anyway, then Nvidia Kepler or Maxwell (GM1xx only) is recommended. For
example, GTX750Ti.
