The number of ways tofullyparenthesize a product is a well known result in combinatorics

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But I'm not sure if this is what the question is after, since from the wording it seems a non-fully parenthsized expression such as (a)bcde would (might?) be acceptable. Anyway I'll give a shot listing out the 14 fully parenthesized expressions

I found it much easier to list the rooted trees rather than the parenthesized expressions. I made an image, they are listed in a systematic order, and you can convert them to expressions accordingly.