Yes, separate the skinks from the eggs. You can incubate the eggs in situ (where they are laid) or take them out and put them in dampened vermiculte in a small covered cup.
Don't turn the eggs over and over - just gently remove them and place a small mark on the top (actually the side), then place in the deli cup, you can bury them half way into the vermiculite.
I would have to look up incubation times, but keep the cup of eggs out of drafts and in a place where it is about 78F for the moment.
Yes, crickets will eat eggs!
Have you done a online search for info on 5-lined skinks? Maybe you could visit this forum:
http://forums.kingsnake.com/forum.php?catid=57
Morgana
Reptayls, Ltd.