If that is your only credit card, then YES it should make a BIG difference! If it is one of several, it depends on your total amount of credit available (mostly). For example, if you had 3 cards with a total credit limit of 15,000 then the $3100 you have balance right now is only 20 percent. Paying it off will still make a difference, BUT if that 5000 card is all you have, then that 3100 balance is 62%!! BIG DIFFERENCE. FICO like LOWER percentages used (but not all cards at zero).
Also, remember that even if you pay off each month AFTER your statement cuts it will still show a balance on your reports. By doing it BEFORE the statement cuts you will show zero, BUT remember to check the account after the statement date to make sure there isnt a small interest charge still owed or something. If you dont make that second payment in a month, you ll get a late!!