take some second hand graphic card for 100 bucks, you will get more than **** HD5670 try find HD4890/4870 or G9800GTX/GTX+ or some G26x/28x if price allow it
or if you can spend more take HD5770 or how its called.
but im afraid about that CPU which your compaq presario have:
AMD Athlon II X2 215 2.7 GHz
Athlon = not much cache, x2= 2cores (can be ok) but 2.7Ghz? its not much AMD dont have such performance per clock speed as intel core2duo, so maybe this could be biggest limitation or even limiting performance of new graphic card.
And you have 250 Watt some cheap power supply (cheap mean that maybe it will not be able put more than 180-200Watts, maybe it burn
) in that machine its another issue which can make bad day after you will put new graphic card inside.
this is why i hate these assembled PCs (Dell, HP...), they dont give much space for upgrading and often are configured to the max (max in terms of its have some part of HW which are on its limit which can hold = power supply)..
We can say that upgrading your PC can be problematic and can cost more than 100 bucks.
I think that better is leave it as it is (mails, youtube, office...) and buy Console or if you have money or will have than buy new one and im sure that lots of people help you pick configuration of HW to fit better for future upgrading and not cost much