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 oil will be just fine, unless your engine is well and truly whipped (overdue for an overhaul), to the degree you have to prop it up with extra-heavy oil while you make arrangements to rebuild or replace it. Doesn't sound like you're at that point, so go ahead; this is a much smarter choice than straight 30-weight.