If you must stick to 5GHz that leaves you with 802.11a and/or 802.11n.
And there are lots of things in the free world that support that.
Look at the ath9k kernel module for your answer:
https://wireless.wiki.kernel.org/en/users/drivers/ath9k
Make a note of supported chipsets, including the single or dual band ones.
Search for those chipsets. I find lots of them very easily.
As an example, when I plug AR9160 (which is dual-band) into a search engine I
find that Sparklan has the WMIA-199NI. That's a Mini PCI card though and I
don't know if it'll work in your machine or not -- maybe it needs Mini PCI
Express for example.
I see that eBay also has stuff.
Anyway, regardless of where you get stuff, those are the research steps to
freedom now that you know the compatible chipsets.
