We should probably stop talking about 5/5/2 openings, because Mandarin isn't one. It's a Mandarin/5/2 opening.
5/5/2 would obviously be amazing if you could open, say, Mountebank/Mountebank/nothing, but you can't, because the first card is Mandarin. Would you want to open Mine/5/2 if you could? Probably not.
When you buy Mandarin with your 5, your deck gains a Mandarin and in exchange you are a turn behind on everything else, because you just doubled Turn 1. So if you went first, you're now going second plus a Mandarin, and if you went second, you're now going a turn later than your opponent plus a Mandarin.
Even if you repeat it 20 times, it's still wrong. You're not one turn behind, what counts (ecept for IGG/Inn) is the shuffle. The correct point would be "one shuffle behind", but this doesn't happen.
The truth is: Mandarin helps you in getting exactly 5 or 6 on your turns 4-6 which helps you getting more of the $5-cards BEFORE your second shuffle.
And yes, in about 75% of all games, I would gladly open Mine/5/2. Even Mandarin/5/2 is good, if there is no serious trashing and at least one other $5 card, I would like to get two of.
But you already get one of them before Shuffle 1, and if you want it that badly, you probably want to be playing it as early as possible. Most of the good $5s help generate more $5 hands on their own, and a lot of them are terminal. Sure, Mandarin is going to make it pretty likely that on turns 4-5, you'll pick up 2 more $5 cards, and you'll have three 5s and Mandarin in your second shuffle. Meanwhile, your opponent picked up his second 5 on turns 3-4, had it in his second shuffle, and used his two 5s to pick up two more on turns 5-6 before he shuffles again. You're now basically even on 5s, he's been playing them more, and you're stuck with Mandarin slowing you down which is a bad thing in the early game.
Let's check this for the base set:
Council Room --> true (+4 cards ~ +2,8 coins), but also helps the opponent
Festival --> might be true, yet no better than silver in gaining more $5-cards (you have 2+ 4 cards with an average of about 0.7 coins which roughly concludes to 5)
Laboratory --> false (you have 6 cards --> average = $4.2)
Library --> just like festival as good as silver
Market --> false (1 + 5*0.7 = 4.5 average)
Mine --> false (1 + 4*0.7 = 3.5 average)
Witch --> false (see Laboratory)
Which of these would be a "first-pick"? Witch is a trap, I'd say. Council Room is good, but only if you're desperately in need of more money and can either buy a good $6 or use the +buy. Library, festival (First-Pick?), Laboratory and Market do help, but not as much as Mandarin does:
Mandarin+Copper+3Estates --> Put back the copper and buy something for $3
Mandarin+2 Coppers+2Estates --> Put an estate back and buy the $5-card you like
Mandarin+3 Coppers+Estate --> Put 1 Copper back and buy a $5
Mandarin+4 Coppers --> Put 1 Copper back and buy a$5 or $6.
Since your money density is below 1 at that point, Mandarin is in any of these cases better then silver!
Mandarin+Terminal --> put the terminal back (except the edge cases where there is only one curse left to deal and you have a curser or where yoe need to get a special card right on this turn before the game ends (Duchy)). Delaying the play of your terminal by one turn usually doesn't change anything, but mandarin grants $3 for that, which should be enough to buy another $5.
