Are you using Embird? It always gives this message when you have a size different from the standard hoop size. I use jef and my hoops for that machine are 126x110 and 240x200. Even when I set it for the larger hoop size it gives that message. So I just ignore it and click on yes when asked if I want to save it anyway and sew it out without a problem.
Same happens when I digitise a design for the large Ruby hoop (200x360). I set the size in Studio, digitise the design and when compiling to a vp3 or vip format I get the message that it does not fit the 100x100 hoop.

I don't use those formats but I'm going to give you a guess. All formats are not precisely the same size in all brands. A 4x4 in pes is actually a fraction under 4 inches because it's actually a metric measurement. I believe a 4x4 in sew is a rectangle and I don't know the exact measurements of it. So maybe it really won't fit the hoops on those formats. Try searching the Internet for exact measurements of the hoops to see if reducing the design size might help.

5x7 is way too large for .sew. I had a 1999 Janome Memory Craft 9000 with a 9x12.5 cm hoop. 5x7 is roughly 13x18 cm so the designs are too large for .sew hoop.
Hugs, Lidia