What'S The Easiest Way To Blast 5000 Sequences Against An Exon Fragment?

I have 5000 EST sequences that I downloaded from Genbank. I have a 500 bp exon fragment that I'd like to BLAST against this lot of sequences to see if my exon is present or not. What's the easiest way to do this?

I thought that there might be a way to do this through the NCBI directly without even having to download the sequences (e.g. an option to 'BLAST these results') but I can't find one. My next option was to download BLAST, setup a local database, import the 5000 sequences and then BLAST my exon against that.

Is there an easier option?

Thanks, John