The Hatters host Brentford on Saturday.
Edwards said: "With the way things have gone, we would take this.
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"At the beginning we knew it would come down to the final five games, we are cool about that, we have spoken about that.
"(Manchester) City was never going to be defining but the next five will be now. We know how important they all are. We know it will be difficult, but our aim is to pick up points in all those games.
"We have had progress this week, whether that means there can be progress on to the pitch now (I'm not sure).
"I don't anticipate too many changes but we are making progress. There will be some players coming back but it will be a struggle for this weekend."