What does 一番 mean in 与5年前相比翻了一番?
翻（了）n番 is common phrase, meaning 2^n. For example, 翻一番 = 2, 翻两番 = 4， ....

But the interesting phrase is 翻n倍. Some would take 翻n倍 = 翻n番, and some would take 翻n倍 = 1*n, and some take 翻n倍 = 1*(n+1). For example, 50翻3倍 could be 150, 400 or 200. This is really a moot point. Personally, I would take 翻n倍 = 1*(n+1) and 50翻3倍 would be 200.