What graphics card does the Pavilion dv5 have?

Not sure... There are many types of that kind of laptop, so therefore there are many types of graphics card too. The best idea to know your graphics card is download GPU-Z

http://www.techpowerup.com/gpuz/

If you are going to buy a laptop, what is your budget?

You have to be more specific about your model, as some models have dedicated graphic processors, whereas others only have integrated graphics.

For example:
HP Pavilion dv5-1235dx has Intel GMA 4500MHD integrated graphics
and
HP Pavilion dv5-1017nr has NVIDIA GeForce 9200M GS dedicated graphics card

Try to google your exact model and read the specifications