Can a player use only the communal cards when selecting their best hand?
In Hold'em, each player makes the best possible 5-card hand possible using any of the 7 cards available. To each player, there is no distinction between the communal cards and their own private cards. The selected 5-card poker hand can include 0, 1, or 2 of the hole cards.

It's possible that the best hand you can make uses 0 of your hole cards. In this case, you cannot win (unless everyone else folds), but if no player can make a better hand than the 5 communal cards then it is a tie.

Background info (prior to edit)

Poker hands, that is, sets of cards that can be ranked by standard poker rules, contain 5 cards. Many poker variants, including Texas Hold'em, give players access to more than 5 cards and let them create the best 5-card hand they can out of all the options. In 7-card stud, some of the cards are private, but face-up. In Texas Hold'em, some of the cards are shared. 

As you said in your question, in Hold'em there are 5 communal cards and 2 hole cards, so each player has 7 cards from which to choose 5 to make the best poker hand they can. The number of ways to choose 5 from 7 is 21 (Combinations, from Wikipedia).

You might think you can get away with omitting the combination consisting of just the communal cards, but this should still be evaluated because if it's the highest scoring hand, then everyone ties (e.g., if the communal cards are a Royal Flush, then everyone ties regardless of their hole cards).