How many monsters should be drawn in a 5 player game during an encounter?
No. The draw 2 rule for 5+ players only affects the number of monsters placed on newly opened gates in the Mythos Phase.

It does not affect the number of monsters drawn at any other time in the game.

The actual rule from the Arkham Horror rulebook (page 10) states:


  Exception: If there are five or more investigators playing, then draw and place two monsters instead of one.


Note that while the rule itself is worded vaguely enough that it could be misread as affecting other cases where you draw monsters, the placement of the rule within the rulebook is specific - this exception is only ever stated within the section that explains the Mythos phase, and is never repeated elsewhere.

The entry in the Arkham Horrom FAQ (page 2) is even more specific about this:


  When opening a gate in a location where there is no elder 
  sign or gate, if there are five or more investigators playing, 
  then draw and place two monsters instead of one.


This passage refers to the page where the Mythos phase is explained, thus it is only ever applied to drawing monsters when placing Gate markers during this phase.