Option 1
Might be easier just repurchasing the Star Trek Season 1 Remastered set (Amazon has them new and used), then try selling one of the sets minus disk 5 to make back most of your money. I mean a used copy is starting out at 15 pounds UK
http://www.amazon.co.uk/gp/offer-listing/B000V0NHEA/ref=dp_olp_used?ie=UTF8&condition=used
Option 2
Failing that, then ebay or contacting CBS for a replacement disk might be your next best bet.
Option 3
If none of that worked, and not that I would advocate it, but if you
could acquire a disk 5 somehow(netflix, a friend, library, etc), you
could rip it ( you can Google a plethora of free DVD ripping software).
I mean if you legitimately bought the set and simply lost disk5, and ripped another legitimately purchased disk 5 just to replace it, and that is all you did, I wouldn't consider that piracy. I think the spirit of the anti-piracy laws is more to prevent people from copying stuff they don't already have and selling it for profit, not to prevent people who legitimately purchased a set but lost a disk from replacing it via software backup, really. But I am no lawyer, either.
Personally, I would go with option 1, though.