Flash is extremely CPU intensive on Linux. Nothing anyone but Adobe can do about that. Adobe decided to render the video in software only, rather than using even the xv output to off load some tasks to the GPU.
For the second part - HD Video.
HD Video is only a class of video which pertains to it's resolution, not it's delivery method, nor codec. If you are attempting to watch streaming flash HD video, see above. If this is mpeg2 HD video, should not be an issue. Make sure you are using the Nvidia display drivers, and a player that uses Xvmc. Xvmc allows the GPU to render Mpeg2 streams while freeing up your CPU. The fx5600 supports Xvmc, but not VDPAU. VDPAU will allow the GPU to decode VC-1, WMV, Mpeg1/2, and Mpeg4-avc (h264). Mpeg4-asp (Divx/Xvid) was added to the newest Nvidia GPUs.
As for other codecs (Xvid, VC-1, WMV, h264, theora ...) this will matter greatly on your CPU. I have a huge gap between my really slow CPUs (PII 450,PIII 600) and slow CPUs (Sempron 3000+ 1.8ghz). The PII and PIII is imposable to play HD videos without the assistance of VDPAU (Nvidia 8xxx+ series card). The Sempron 3000+ 1.8ghz can render 720p (1280x720) videos, 1080P is out of the question. A dual core e8400 (3.0ghz x2) can handle 1080p HD without GPU assistance, as well as streaming flash from Hulu - which they call HD.
It boils down to, you either need a CPU less than 3-4 years old, or an Nvidia graphics card that supports VDPAU to achieve flawless HD rendering. There are tricks and options you can pass to mplayer (-lavdopts skiploopfilter=all), and using the multi-threaded ffmpeg for decoding if you have a multi-threaded CPU.