rickson23, 19" Display resolution is normally 1440X900. At this resolution HD 5670 can play games you have mentioned with high setting. And Topgear has recommended the 512 MB version because the performance difference between the 512 MB and 1 GB version is really very very low. The reson is these lower-mid range cards cannot utilize full 1 GB of memory.
However, if you want something little better then get the HD 6670 1 GB GDDR5 around 5K. Chose from brands like MSI or Sapphire. This card is based on Northern Island architecture and offers performance very closer to HD 5750/6750 or GTS 450.
@topgear: why 512mb,why not 1gb ddr5 ?