Stripped screws on laptop?

I'm considering upgrading the memory on my Lenovo G560 laptop. But it seems like 5 of the 7 screws I need to unscrew to access the memory are stripped.

The screws start to come up, but then go around in a circle and I hear a clicking noise with my screwdriver. That's where it ends.

What are my options? I'd be a little nervous about drilling.

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