Well it's tough to say, since we all have different tolerances for rides. My wife seems to be similar to you... she does not do coasters at all, and dislikes drops.
My honest opinion is that BTRR is not scarey... no big drops of any kind, and is lots of fun. Try it once and see if you like it. Note, my wife has not tried BTRR. But in the line, I came across many who are not big on coasters but tried BTRR and liked it.
Splash mountain has a wonderful story, and the drop is really not as bad as it looks -- it's not a fast drop. My kids finally convinced my wife to try Splash Mountain just once to see the story inside. Well my wife tried it, and she agreed the drop wasn't quite as bad as it looked, and was glad she tried it. However she wasn't about to try it again and again!
Space Mountain doesn't have any big drops, and if you take away the fact it's dark with lots of lights, it's really not too exciting of a coaster (I know, heresy to say that on a Disney board). But if you don't like coasters, just pass on Space Mountain (unlike Splash Mountain which has a nice story to it, it's SpaceMountain is just a coaster, and why put yourself in a long line if you don't like coasters).
If your child is excited to try a ride, and meets the height requirement, then he should be fine. However, I don't think a 5-year old is likely to meet the height requirement for Splash Mountain (or Space Mountain). BTRR might work though.