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  Meg Lanning hit a composed 55 and Alyssa Healy a rapid 25 as Australia compiled 132-6 amid a mixed England fielding performance.
  In reply, Charlotte Edwards (31) and Tammy Beaumont (32) added 67 for the first wicket inside 10 overs.
  But, from there, England lost regular wickets to slump to 127-7.
  Australia - seeking a fourth straight title - will play New Zealand or West Indies in the final in Kolkata on Sunday.
  England, meanwhile, miss out on the final for the first time since 2010.
  Although they arrived at this semi-final having won all four of their group matches, England had already shown plenty of fragility with the bat, collapsing from 59-0 to 109-9 against West Indies and from 42-1 to 92-8 against India.
  This time, their middle-order woes finally cost them as they squandered the perfect platform laid by Edwards and Beaumont.
  With seven overs remaining, England needed 45 more with nine wickets in hand, but they succumbed to panic.
  First Beaumont played an unnecessary slog and was caught at cover, then Natalie Sciver was bowled third ball attempting an overambitious scoop, before Heather Knight smacked Erin Osborne to long-on.
  From there, England's hopes rested with the out-of-form Sarah Taylor, but her dismissal - caught behind tamely trying a reverse sweep - summed up England's muddled thinking and sealed their demise.
  After Healy and Elyse Villani got Australia off to a superb start with a partnership of 41 from 27 balls, the Southern Stars were in danger of faltering when both openers were dismissed in quick succession.
  Lanning came to the crease having passed 30 only once in four innings in the tournament, but the world's top-ranked T20 batter quickly set about demonstrating her class.
  Scoring heavily behind square on the off side, Lanning hit six fours, adding 36 with Ellyse Perry.
  As England came back into the game with late wickets, the Australia captain remained a serene presence at the other end - but she could not find any boundaries in the final four overs of the innings as Australia lost momentum.
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  It was a mixed performance in the field by England, containing both moments of magic and costly instances of ineptitude.
  In the closing overs, Sciver brilliantly ran out Alex Blackwell with a direct hit from deep midwicket, and Anya Shrubsole then accounted for Lanning with another superb piece of fielding, shattering the stumps from long-on.
  However, earlier Edwards' side had fluffed two straightforward run-out chances, with Lanning reprieved by a poor Danielle Wyatt throw and Blackwell surviving after a Shrubsole fumble.
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  Crucial runs were also conceded by poor ground fielding, with the whole haphazard display summed up by the comical moment when an inattentive Sciver was hit on the head by Katharine Brunt's throw as she walked back to her bowling mark.
  England captain Charlotte Edwards: "I think we know a lot about each other and there are no secrets but Australia held their nerve and we didn't, and that is probably the difference.
  "We didn't start particularly well with the ball but dragged it back and then started brilliantly with the bat and then lost our way. We showed glimpses towards the end of getting it back, but it wasn't quite meant to be."
  Australia captain Meg Lanning: "We knew the powerplay would be crucial and with the start we got, we got ahead of the game. We knew it would be more difficult when the ball was softer so it was crucial we built on that momentum.
  "We didn't start as well as we would like with the ball but we began to hit our lengths and the stumps."
  England coach Mark Robinson: "It is a cruel game, another five runs then we were in a super over. Well done to Australia on the day
  "There is a little stage fright and we were a little guilty of that in field, but we are not fit enough. Athleticism is a gift, so there is not much we can do about that, but anaerobic fitness we can do something about and we will."
target: England were knocked out of the Women's World Twenty20 by Australia for the third tournament running with a five-run semi-final defeat in Delhi.