Measuring 12 V via voltage divider: choosing the right resistors
What you are looking for is called the Thévenin equivalent source.
For the schematic you are showing, and assuming you can neglect the
output resistance of the battery itself, the output resistance of the
voltage divider is the same as the two resistors in parallel. If you
want the maximum allowed resistance (minimum current) you have then to
solve:

1/R1 + 1/R2 = 1/(10 kΩ)
R2 / (R1 + R2) = 5/12

which gives:

R1 = 12/5 × 10 kΩ = 24 kΩ
R2 = 12/7 × 10 kΩ ≈ 17.1 kΩ

You can then round the values down to the closest standard values,
taking care that the rounding does not impose more than 5&nbsp;V on the
analog pin. For example, if you restrict yourself to the E6 series, you
could choose

R1 = 22 kΩ
R2 = 15 kΩ

which would give you a Thévenin equivalent output resistance of
8.9&nbsp;kΩ, and a maximum output voltage of 4.86&nbsp;V.