For something like let's say an Earth Elemental that has a DR 5/-, what weapons can bypass that DR? I understand that all spells will still do full damage against the monster but I am particularly curious about magical weapons and weapons with special abilities and/or special materials. Because from my understanding if a monster has a DR that is bypassed by a magical weapon it is usually marked as DR 5/magic (and similarly in the case of a special material).
The – indicates that the damage reduction is not bypassed by any weapon. All weapon damage is reduced by that damage reduction. Damage reduction that is bypassed by magic weapons, weapons that deal bludgeoning, piercing, or slashing damage, weapons of a certain material, and/or weapons with a particular alignment, those all indicate that after the slash, and the – in this case indicates “none.”
As explained in the Universal Monster Rules in the Bestiary (copy found at d20pfsrd)
When a damage reduction entry has a dash (—) after the slash, no weapon negates the damage reduction.
The other two answers pretty much cover basic damage. The only way to "bypass" DR/- is by doing damage that DR does not reduce. A flaming weapon does its fire damage as normal. "Damage Reduction does not negate ... energy damage dealt along with an attack."