Connecting an external Video Card to my laptop.

No.

No.

No.

To all your questions.

Not even if I open my computer and connect some (I don't know) adapter?

There are USB external video cards available. You would need to see if they will do what you need. I looked into them years ago, but they did not look too good. There is no other way to change the video hardware.

I've looked it up but it only gives me adapters from USB to HDMI or VGA...

there is no adapter for desktop Video Card? [:'(]

Well thanks... I'll just buy a normal PC with a video card that's good enough for gaming...

The only practical external video adapters (and bear in mind these ONLY work with external monitors, so they turn your system into a glorified desktop anyway) require an external ExpressCard slot your system doesn't have.  And by the time you buy the box plus the video card and external monitor, you're up to what a decent desktop system costs anyway - so that is a better option.  If you want to spend $500+ on a video upgrade, buy a new desktop system (your system doesn't have the external expresscard slot anyway).

I recently purchased a second hand Riser PCIE 1X TO 16X adapter to start a eGPU build. I was wondering if I would need an express card connector for this to work. I have a 2007/08 Dell XPS M1530 running Windows 10 64 Bit. I'm also currently looking into what graphics card to use. The adapter has a USB 3 connector cable aswell if that means anything. 

Here is the adapter. www.amazon.com/.../B00MTI3K62

I doubt there is a 1x slot inside the M1530. Even if you could, the 1x speed is too slow for meaningful graphics, and the riser must have a separate power supply. See this post for some info; they used an express card connection in some systems. I agree with an earlier poster. You could get a low cost Win 10 laptop for $300 os so that would outperform the modified M1530. 

http://forum.notebookreview.com/threads/lets-figure-out-how-to-make-a-diy-egpu-previously-diy-vidock.397667/

There IS a PCIe-3 port in your laptop (I've got the same). And you actually can use the desktop video card adapter which is I'm going to do as well quite soon (I'm waiting for adapter delivery). The only problem is that you will need to get rid of your wifi adapter and use only cable.

I don't know what all those people are talking about, probably they don't have Inspiron 5720 or just blind.

Are you saying I have to go directly into the laptop motherboard to remove the adapter card? Or are talking external, because the M1530 has it built in.

I see you have an XPS M1530. I too have one and am trying to do a eGPU setup myself. I have an external PCIE board with a USB 3 cable that is connected to a PCIE connector. I'm not looking into doing anything fancy, just wanting a better GPU for my PC until I have the time and money to build a full PC from scratch. This is what I have so far, 

www.amazon.com/.../B00MTI3K62refRID=DZEZR6Y9N7VJRR4Q76D3&;ref_=pd_ybh_a_48

Are you talking about the Dell XPS M1530? If so, then I currently use it as a desktop and have it connected to my network via cable. Removing the wireless card wouldn't be an issue, but would I be able to close the back of the Laptop after I connect it to the adapter?

Not without cutting some holes in the case to route wires -- and given how tightly packed the internals of the systems are, even that's a big gamble.

The M1530 came with either an Nvidia 8400 GS or 8600 GT video card. These should work foe non-demanding games. The 8600 GT is supported up to Win 10 for a video driver. The 8400 GS should also be supported. These are Win 8.1 drivers.