You have a decent chance of prevailing in court but there is some conversation alluded to in your posts that I am not privy to. Depending on exactly what that is, it could mean nothing or it could be damning.

As I said, if your move in date was the 4th or 5th, if she refused to allow access at that time, she has breached the contract. The problem is what would a judge do if s/he heard you were offered the keys on the 6th or even the 7th. Especially since you have not contracted for another place, you're argument of having to move in by the 5th doesn't mean a lot since you have not moved in anywhere nor have you contracted to move into another place yet.

As t whether she would take you to court is something only she can say. You did ask about how to get your money back. There are only two things you can do: 1/ ask her and then, if she refuses 2/ sue her. There is a third alternative which would be to walk away but that is all up to you.

and your move in day wasn't last week. It was Wednesday or Thursday of this week as to day is only Saturday the 7th. Another point that may work against you was your claim you had to start moving in by the 5th. A judge may look at you and ask: what happens if you don't? (and realize that you have not moved in anywhere starting on the 5th). In other words; how has the delay injured you? If there is no injury, a judge could rule the delay effectively is meaningless and not a great enough breach to allow a termination of the contract.