A-5 Triple draw beginner's question

I just started playing A-5 triple draw and I have a basic question about playing on the button. I was dealt A257K on the button. Everyone limped, so there were 5 players in the pot. I have the following questions:
1) Should I have raised? (I didn't raise)
2) Everyone drew 2 cards. I tossed the 7 and the K. Should I have kept the 7 and drew to the 7 low or was I right to toss it? I figured that the 7 wouldn't have held up in a multi-player pot even if I did hit it.
3) The second round went Bet, call, call, call and I folded because I blanked. Was my fold here correct? I've been operating under the assumption that I need to improve on every draw. So far, I've been playing hands that I can draw 2 to a 5 or 6 low and if I don't improve I'll fold on the following round. But sometimes I get tempted to call on without improving. Like in this case, I'm drawing 2 to a 5, but there was a lot in the pot and it looked like a lot more would come, plus I've got position. So maybe in this spot I should have called? I'm a BEGINNER, so go easy if my thinking is not correct. I don't really know what I'm talking about....

[MarkGritter]

I would probably raise from the button. I don't understand why you say there were 5 players in the pot--- the blinds have not yet acted, so there are only 3 limpers ahead of you. It is generally worth trying to keep the blinds out. And you have three to a wheel, which is likely to have a small equity edge against three limpers. You would certainly play this hand against a raise.

The only reason to not raise here is to manipulate the pot size. This is not something you should be worrying about as a beginner. Your hand is strong enough to be betting for value.

Tossing the 7 is almost certainly correct here, although some might argue that the deck is sparse due to the number of players, so it is OK to play it. I think you want to be drawing very smooth in a multiway pot. You can reconsider if you get another 7 on the draw.

You don't have to improve to call a single bet here, particularly if you are closing the action. If there was a raise the first round the pot would be certainly large enough to take another card off. Even here you are getting 9:1. That's huge. You are about 40% to improve to a one-card draw when you draw two, and a bit less than 10% to draw two good cards. (Possibly less because of all the low cards that are already out there.)

In general you can take a card off whenever you had a legitimate starting hand, brick, and face only one bet. If you are stealing or defending there are situations where a fold is appropriate. But, if you always fold unimproved to a single bet the second round you are folding too often and your opponents can use that against you.

So I should be calling more and drawing 2 on the second round in a multiway pot if I'm in late position. I guess I'm playing too tight. What about if i'm only drawing to a 7 in this spot? Say I had A27, would I call a bet on round two to draw two cards?