Im very familiar with Iron Gods, its one of the adventure paths that is a high priority on my list of campaigns to GM. As such, I identified the construct you mentioned right away (Gearsmen), and I will say some spoilers about their behavior that you might not want to know, so skip ahead if you don't want spoilers:
Gearsmen will not pursue or attack enemies outside of the area they activate, so they could be tricked into being activated ("intruder detected! exterminate!") and kited to the door so the group can handle them easily. They are also mentioned as being a "tough enemy" for the group by the designers, so they are intentionally difficult so the group will thankful when they get energy weapons later in the adventure. Also note that they can repair themselves, they arent always skippable, but sometimes you simply have to handle them temporarily and later come back to try to handle them permanently, so keep that in mind. Also, the adventure does not hand you any electricity weapon, so don't expect to kill them using that unless you manage to lure them into one of the several electricity traps.
With that out of the way, the easiest way to handle high DR (or hardness, in this case) is to obtain ways to cause Energy Damage, easily available from spells, alchemical items, and certain class abilities. To list a few easy solutions (and please, this is not an exhaustive list, but merely examples):
- Tanglefoot Bag, will entangle them and prevent them from attacking the group;
- Alchemist Fire, 1d6 damage on a direct hit, and another 1d6 on the next round;
- Acid Flask, 1d6 damage on a direct hit, a cheaper alternative to alchemist fire;
- Bottled Lightning, 1d8 electricity damage;
- Shocking Grasp, 1d6 electricity damage per caster level on a melee touch attack;
Hardness on creatures work a little differently than on objects (as explained on this answer, which is talking about Iron Gods's robots, by the way), as energy damage is not halved against them, and any energy damage caused is then reduced by their hardness value. This means that you want to use whatever energy type they are vulnerable to, as others will get reduced by 5/10 points and not really be effective.
Robots specifically are also vulnerable to electricity, so try to find a way to obtain a reliable source of shocking grasps, or bottled lightning and you will be golden. Not only they will take increased damage, but their Hardness will not apply. Acid flasks and alchemical fire won't really be a good idea against robots, as they are not vulnerable to fire or acid damage.
Constructs, in general, usually have a low Dex score, and bad reflex saves. This also means they have a low Touch AC, being easy to land touch spells and abilities on them, including alchemical items like those I mentioned (ranged touch attacks for thrown alchemical weapons).
Another spoiler about treasures from the adventure:
The adventure will give you a few energy weapons, such as grenades and timeworn weapons (flare guns), which can be used a few times and cannot be recharged. Those might help since they also bypass hardness/damage reduction. The adventure is pretty hardcore on damage, but you also get a lot of technological treasure, including a healing gun (!).
Another way to try to handle them is to group up and abuse maneuvers. For instance, disarming them will prevent them from electrifying their weapons, drastically reducing their damage output. Dropping prone and/or grappling one of them would allow other party members to have an easier time trying to land their attacks.