There isn't going to be an easy way to get your child to stop using the pacifier because she has been using it for way too long. However, nothing is impossible with God. This will just take perseverance on your part. Here are my recommendations.
My recommendation for parents who need to ease their children into changes:
1st: You have to stop calling the pacifier a binky. Your daughter is old enough to use the proper names for things and to understand that a pacifier is only for little babies.
2nd: Let her know that she will soon not be using a pacifier anymore because she can find other ways to soothe herself.
3rd: Restrict the pacifier to bedtime only and then stop bedtime use after about a week.
4th: Never mention the word binky again or pacifier as it relates to her.
My recommendation for parents who like to "get it done"
1st: Tell your child that she will no longer be using the pacifier since she is a big girl.
2nd: Take all of the pacifiers from her and never, never, never, give them back to her again. She will cry, pout, scream, shout, lose some sleep, refuse to eat, etc. but she will get over it. She will NOT have emotional damage as a result... I know this for a fact.
3rd: DO NOT try to appease her by telling her that she will get something in its place as this will cause her to become dependent on something else.
The hard part about being a parent is preparing our children for the next stage of life. Your daughter will be better prepared for being an active participant in life if she is able to handle life without a crutch. Best wishes to you and I hope that whatever you try works.