I'd go farther than LVM and say that significance/nonsignificance isn't really a good reason for including or dropping ANY variable, although it is one that is often used. I've had bosses/clients insist on it. Effect size is more important. With a large N, as has been said, it's easy to get significance. And, as also been said, the intercept is usually not of interest, but that is a reason for leaving it IN, not taking it OUT.
With 5,000 cases and 15 IVs, unless the DV is very unevenly distributed, you have plenty of cases per variable. Why not include ALL the IVs? How did you choose them in the first place? Are they substantively important?
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