Is there a way to connect a Nvidia GEFORCE GT 710 to my Inspiron 14 5000 Series even with the lid open?

When you say "bottom lid", do you mean the underside panel that exposes hardware like the RAM modules, hard drive, etc?  That's not really a good idea, but the only way to get a desktop GPU connected to a laptop is to put the desktop GPU into a PCIe enclosure that connects to your system either via a ribbon cable that plugs into a spare M.2 slot inside your PC (if you have a spare one) or via Thunderbolt 3.  The Akitio Node is a Thunderbolt 3 external GPU enclosure, for example.  But I don't think the Inspiron 14 5000 has any M.2 slots at all or Thunderbolt 3, although even if it did, that's still not a guarantee that the system would actually work properly with an external GPU.

No way - no how.