Unless otherwise specified resistances to the same element do not stack, and you simply use the highest resistance to that element. This is a [general rule][1] that still applies in this situation.

> Stacking refers to the act of adding together bonuses or penalties
> that apply to one particular check or statistic. Generally speaking,
> most bonuses of the same type do not stack. Instead, only the highest
> bonus applies. Most penalties do stack, meaning that their values are
> added together. Penalties and bonuses generally stack with one
> another, meaning that the penalties might negate or exceed part or all
> of the bonuses, and vice versa.

Note that [the rules on bonuses][3] do not exactly apply here, as resistance and damage reduction are not bonuses. However the rules for energy resistance specify that “Each resistance ability is defined by what energy type it resists and how many points of damage are resisted.” - thus the energy type defines if it stacks or not. I.e. fire resistance 5 stacks with cold resistance 10.

However, the [rules on Damage Reduction][2] are very clear that multiple damage reductions do not stack, though with multiple sources of DR, you can choose which weaknesses apply (two sources of non-overlapping DR are effectively typeless):

> If a creature has damage reduction from more than one source, the two forms of damage reduction do not stack. Instead, the creature gets the benefit of the best damage reduction in a given situation.



  [1]: https://www.d20pfsrd.com/BASICS-ABILITY-SCORES/GLOSSARY/#Stacking
  [2]: https://%20https://www.d20pfsrd.com/Gamemastering/special-abilities/#TOC-Damage-Reduction
  [3]: https://www.d20pfsrd.com/basics-ability-scores/glossary#TOC-Bonus