No, your graphics card should be sufficient. (EDIT: Sorry, I mistook the graphics card, it actually might be the problem) Maybe it's a Win 7 64 DirectX issue.

First of all update your graphics drivers to the newest version.
Then install the DirectX9 Redestributable package from Microsoft:
http://www.microsoft.com/en-us/download/details.aspx?id=8109
(Extract the files to a separate folder and run dxsetup.exe)

If the game still doesn't run fluently, hardware acceleration for 32 bit DirectX might be turned off on your system.
Here's a thread that explains how to check and activate it:
http://www.gog.com/forum/the_witcher/fix_minimum_requirements_not_met_on_win7_x64

No, the graphics card and the CPU are very much the problem. If you had a problem with DirectX hardware acceleration being disabled, you would have gotten an error, and the game would not have started.

The R5 230 barely matches minimum spec when compared to cards that were current when the game came out. Figure on medium settings but turn off AF and AA.

The CPU has to be able to process all the actors in one thread. It will often run with one core at 100%. The faster that core, the better the frame rate. Scenes like the Vizima Trade Quarter will show this up. And, to put it bluntly, lesser AMD FX cores really suck hind teat.

I fear cjrgreen is right about the graphics card. I mistook it for another, more recent one with 2 GB memory. Thanks for pointing this out cjrgreen. Benchmarks show that my old Sapphire HD 4870 is way more powerful than the Radeon r5 230. So it might be the bottleneck. I'm not so sure about the processor, as mine is even older and did a good job. Eventually it's also about resolution, the higher, the more graphic processing power is needed. If you want to raise graphic enhancements you'll need to lower resolution. Anyway, I'd suggest the opposite, raise the resolution and refrain e.g. from using strong Anti-Aliasing techniques. Multiple AA is not necessary when resolution is higher. The visible enhancement is marginal, but it'll strain your graphics card.