Does EFUDEX have a recommended shelf life? I have two tubes prescribed in 2005 and stored in a?

YES, here's what I googled "The recommended shelf life of Efudix cream is 60 months. Shelf life after first opening the immediate packaging: 90 days for the 20g and 40g tubes."

I only used a small portion of the 40 g tube I had opened a year ago, now after applying the cream to my nose for almost three weeks, it's evident the potency has been drastically reduced to the point of being ineffective, opened tubes expire especially rather very quickly, unopened remain good much longer.

Yes, Efudex will have a shelf life and if you look closely you should be able to find it - probably stamped on the bottom of each tube.

If it has past the expiry then the safety and efficacy of the cream can not be guaranteed. They should be thrown away.