Generally, when a crochet pattern says to crochet into a "space" (or "sp"), it means to crochet on the chains that create a space. According to the pattern you've quoted here, one "space" is the "ch-3 sp" (a chain of three stitches that spans a space) and another space is the "ch-5 sp" (a chain of 5 stitches that spans a space).
So you would crochet a single crochet on the chain 5 stitches that span the space. This single crochet will wrap around the chain itself.
However, since I don't have the previous row instructions, I'm not sure exactly what the next "space" is--a ch-5 space or a ch-3 space (or something else, maybe?).
At any rate, patterns are written like this to distinguish between crocheting into a chain (for example, into the third chain of a chain 5) vs. around the entire chain itself.
If this is still unclear, let us know and we'll try to unconfuse you some more!!