Question 1180664
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Technically, the question can't be answered, because you did not specify the number of cards.  If the game is played with a standard deck of 52 cards, you need to say so in the statement of the problem.<br>
I will assume the cards are a standard 52-card deck....<br>
Use the basic definition of expected value.<br><pre>
           probability    value (winnings
                       minus cost of playing)
  -----------------------------------------------------------
 winning card  2/52    -5+20 = 15       (2/52)(15) =   30/52
 other card   50/52    -5              (50/52)(-5) = -250/52
                                    -------------------------
                                     expected value: -220/52<br></pre>
The expected value for playing the game is -220/52 dollars, or about -$4.23.<br>