Slant Six Oil light coming on — need a new pump?

Can I use synthetic, or no? I happen to have a bunch of 5w-30 full synthetic. Pennzoil Platinum synthetic, to be specific.
That'll work very well. Just keep your eye on the dipstick at first. That oil has a high natural solvency, so it will keep cleaning. If it quickly turns black, change it and the filter. Keep that up until it slows turning dark.