Gunk in coolant reservoir

I own a 92 Cadillac Eldorado with 150K. The radiator itself is basically overflowing when I take the cap off with very clean, fresh looking antifreeze. However the overflow has grimy residue all on the inside of it, and when I look down into it the fluid in the overflow is very dirty and grimy. I'm just wondering if I should be concerned or ignore it. Should I flush the whole system thoroughly or just remove the overflow and clean it out?

Any help is appreciated.

Thanks,

Mike