Me again, sorry for the delay.
I finally worked it out. My connections were fine, my mistake was to plug the capacitors too far from the 5V and the ground. Moving the cables closer to the source fixed it.
It might also be worth mentioning that the on the first try, both digits flashed for a second and went blank again.
My second mistake was to test with a 10K resistor. Using 51K resistor was the solution (I'm using displays with an optimal Forward Voltage of 2V, and a DC forward current of 20mA).
Hope this helps someone, it took me way too long to solve this - but finally, it's all fine.
Thanks guys ! 