Question Will this graphics card fit in my HP rp5800?

[YouTownsPerson]

So I just got a refurbished HP rp5800, and I found out it will not run Minecraft. I am considering getting a cheap but good enough graphics card, such as an EVGA GT 710 2GB DDR3 64bit Single Slot, Low Profile 02G-P3-2713-KR. I am new to computer components and PC building, and I do not know if it will fit in my computer. I have attached pictures of my computer. Will it fit, and will it run Minecraft? Edit: somethings wrong with the image tool, so I uploaded to Imgur.

 

[Groveling_Wyrm]

You will need a half-height graphics card. The one you listed should fit with the smaller plate.

You will also need to ensure that your power supply can handle the new Graphics Card.

 

[YouTownsPerson]

Well, now I don’t know if this is possible.
My power supply does not exceed 240W, the card is 300W, and I cannot find another supply that looks like it will fit. I also can’t find out what kind of motherboard it is, so I can’t just buy a new case. What should I do?