I’m in an introductory accounting class, and I’m comparing the
financial health of two companies.  It seems like most of the ratios
we’re learning in class depend on numbers that are wide open to
manipulation by managers.

I’m looking for five indicators of financial condition that I could
use to measure and compare the health of the firms, as well as
explanations of how to use each of the indicators.  I would like
recommendations for indicators that are based on accounting data found
in annual reports.  I’m looking for the best available financial
health indicators for reducing the impact that managers’ shenanigans
have on accounting data.

I’m not looking for originality - just utility and clarity.

It is MUCH harder to manipulate cash than just about anything else, so
"follow the cash". Learn how to discern cash flow and focus on ratios
that relate cash to something else. Of course, you'll want to consider
how easily the "something else" in those ratios can be manipulated as
well.