What video cards and processors can my HP Compaq DC5850 pc fit?

For the video card it depends if it's a microtower (can take a regular PCIe x16 card) or small form factor (can only take a low profile PCIe x16 card). -> check this website to find out -> http://www8.hp.com/h20195/v2/GetDocument.aspx?docn...

Also, the video card options are limited by the power supply. The higher-end video cards require at least a 500 watt power supply. The 5850s include either a 300 watt (microtower) or 240 watt power supply (small form factor) And, depending on the PC form factor, there may be limited options to upgrade the PSU as well.

Your best choice for video cards, assuming a microtower, is probably the GTX 750 Ti. This will most likely not require any upgrades to your current system although it will be stretched to its limits.

As for CPU, the best you can do with the current motherboard is to upgrade to an AMD Phenom X4 9850B processor.