1. Go to Taxonomy: http://www.ncbi.nlm.nih.gov/Taxonomy/Browser/wwwtax.cgi?mode=Info&id=5833&lvl=3&lin=f&keep=1&srchmode=1&unlock
2. Choose Nucleotide 87,341
3. Send to > File > Fasta

Do you really need to use eutils? If your starting point is a file of sequences, Adam's answer is perfectly good.

If you do want to use eutils, as part of a larger program, you need to read the documentation and decide on a programming language. In particular, you need to understand efetch. The documentation includes an example in Perl for fetching many sequences from a given organism.

Thanks to Adam's suggestion, I have found a way to do this. It seems that I can use 4 different "term" expressions in my esearch query:

• term=txid5833 will result in just retrieving sequences with this txid.
• term=txid5833[Organism] will return all the sequences with this txid, and all its sub-txids.

Interestingly, it is possible to add modifiers to the tag:

• term=txid5833[Organism:exp] has the same result as the tag without the modifier.
• term=txid5833[Organism:noexp] has the same result as not having the tag at all.

So by adding the field tag (with or without the modifier) to the txid is what I needed: term=txid583[Organism:exp]. I'm guessing the "exp" modifier stands for "expanded". These tag modifiers are probably documented somewhere, unfortunately, I can't find it anywhere. If someone does, please add a link to it in the comments.

The resultant query is this: http://eutils.ncbi.nlm.nih.gov/entrez/eutils/esearch.fcgi?db=nuccore&term=txid5833[Organism:exp]&usehistory=y

This retrieves the list of all the sequences I am looking for. I can then use efetch on that list to retrieve all the records I want.