Archer says while showing the ship that they've been in space for "4 months, 3 weeks, and 6 days" -- assuming a month to be 30 days, that would be 147 days. At Warp 5, the farthest the ship could have gone during that time frame is almost exactly 50ly. In reality, by the side-jaunts, they should be notably closer to Earth than that, especially since they've also not been at Warp 5 the entire time. There are roughly 1300 star systems within this volume of space containing 1800 stars.