め after a counter implies some sort of ordering, right?
Say that you are shopping for a cat.
You look into a room with 5 cats in it. Does saying
五匹めが好きです。 mean anything?
In that context, saying
I like the fifth one. sounds ridiculous.
You look into a room with 5 cats in it. Then you have a dialogue:
Could that mean that "B" likes the smallest black cat? The ordering is implied to be size?
I like the fifth one. does not make sense.
I like the fifth **smallest** one. makes sense.
五匹めが好きです。 only makes sense when you use context to imply in size as the ordering criteria.
You are, one by one, shown 5 cats. Then you say
五匹めが好きです。 And that means that you like the 5th cat that was shown to you? Showing the cats sequentially tees-up time as the criteria. There is no need to establish context.
You are, one by one, shown 5 cats. Then you have a dialogue:
Now, we have 2 possible ordering criteria. Since size is explicitly established as the immediate context, implied "size ordering" supercedes the default "time ordering"?