This should be a really simple question but - can you 5-foot step while entangled in Pathfinder.

I can see arguments both ways as to whether you can but I cannot see anything definitive.

5' step says:

You can only take a 5-foot-step if your movement isn't hampered by difficult terrain or darkness. Any creature with a speed of 5 feet or less can't take a 5-foot step, since moving even 5 feet requires a move action for such a slow creature.

Entangled says:

The character is ensnared. Being entangled impedes movement, but does not entirely prevent it unless the bonds are anchored to an immobile object or tethered by an opposing force. An entangled creature moves at half speed, cannot run or charge, and takes a –2 penalty on all attack rolls and a –4 penalty to Dexterity. An entangled character who attempts to cast a spell must make a concentration check (DC 15 + spell level) or lose the spell.

It says they move at half speed, and specifically mentions run or charge but does not mention 5-foot step at all.

But 5-foot step implies (without saying so) that halved movement prevents you doing it.

Is there anything I've missed? Right now by my reading RAW says you can do it but I may have missed something.