How to solve system of BIG equations?

Hello everyone!

how to solve system of 5 equations like as in attachment, but much more faster?

I tried to do this on my computer (CPU 8 Core 3,4 GHz, RAM DDR3 2x8 GB, SSD) but after 12 hour my computer doesn't respond.

What I can do if I don't have a supercomputer?

Forum.mw