Specifically, I'm trying to calculate the best way to get
close to 5250 Ohm, using E12 preferred values. Power consumption
is not an issue and I'd like the value to be +/- 2% as that's
the resistor tolerance.

Not an answer to your question, but sticking a 4k7 resitor in series with a
1k pot would be my solution.

Oh, and yes, programs to do exactly what you want have been around for
years. I wrote one. In Fortran. In 1979. I'm pretty sure I have the punched
tape somewhere around here ... ;-)

These days I'd just muck about in Excel and use goal seeking or whatever to
get the answer.

Al.