OHGrandma, so glad he found something he likes! Those are pretty fun ones--I was a ten-year-old mystery fiend myself (and I haven't really grown out of it)! When he runs out of those, you might try Rex Stout's Nero Wolfe series--perfect for that age and stage, I think. I also liked Perry Mason at that age (though it seems to me that there may be some more adult-type situations in those than in NW).

Shellymos, a possibility or two after the Narnia books might be Edward Eager's books, or LM Boston's Green Knowe books. Both fantasy series, but on the less scary side as those kinds of books go. (The Green Knowe ones are more suspenseful/mysterious than the Eager ones, but still well within my personal comfort zone for young-kid scariness.) "Tom's Midnight Garden" by Philippa Pearce is another excellent fantasy choice.

I would say Lloyd Alexander's Prydain chronicles are too scary for 5, but some of his other books might suit--Time Cat, for instance.

Some kids seem pretty taken with Cornelia Funke's fantasies (Harpo was keen on her books a few years ago); I haven't really warmed up to them myself yet, but they might be worth a go, too.