Confused about network unlocked,carrier unlocked,factory unlocked
Yes, but not Necessarily any carrier.

Network unlocked, carrier unlocked, factory unlocked all essentially mean that the phone can be used on any carrier that model is designed to work.  There is different meaning factory unlocked suggests the phone was never carrier locked and bought directly from Apple for the full retail price.  Carrier unlocked suggests that it was once locked to a carrier and has now been unlocked.  Network unlock could mean either.

Determine the exact model number of the phone. For an iPhone 5 it's likely A1428 (GSM) or A1429 (has both CDMA and GSM models).

Consult this table on Apples website to see which models work on which carriers by country.  (You will need to scroll down considerably to reach the iPhone 5 section.)

The model number is printed on the back cover of the phone. Source Apple Support Article HT201296.

A1428: iPhone 5 (GSM model)
A1429: iPhone 5 (GSM and CDMA model)
A1442: iPhone 5 (CDMA model, China)


FWIW, if you're considering purchasing this phone used you should request proof that it is carrier unlocked.  

You should also use Apples Activation Lock tool before buying to ensure that the findMyiPhone is turned off.  If the activation lock shows on the phone will be of no use to you, until the original owner releases it.  This is different than the carrier locking.