Considering the prevalence of bluetooth on cellphones, headsets, mice, gps, etc., I am amazed at how few laptops just come with the damn things built in. Seems like the european and asian versions of a lot of the exact same models sold in the U.S. will come with it, but they nix it from the U.S. version.
Depending on the exact model of your 5610 (there are different models in the 5610 line) you may be able to get one from acer. I believe Acer is one of the companies who, as above, have bluetooth available/standard on some of their foreign market versions, iirc, so if you can manage to talk to the right person at acer, they can probably figure out the part number and order it for you. Doesn't seem to be on their website though. Path of least resistance would be to give them a call and see what they say. They should at least be able to tell you the form factor, anyway.