Mark Noble believes the Hammers can edge closer to the top ten with victory at Arsenal on Tuesday.
The Gunners reached the FA Cup final on Saturday, but Noble says the Hammers possess the ability and self-belief to pull off a shock result at the Emirates Stadium.
He thought the performance in defeat to league leaders Liverpool merited more and if they put in a similar display they will be rewarded.
"Against Liverpool we put in one of the best first halves we've played this season," he said.
"We were unlucky to lose the game with a penalty that wasn't, but it was nice to go out there knowing we were near on safe and could enjoy it.
"I thought that showed and hopefully we can get the same attitude on Tuesday.
"Our aim since the start of the season has been to at least match last year's finish.
"We didn't have the best of starts, we know that, but since Christmas we've really dug in and put the points on the board. That's what has made us half-safe now.
"There's five games left that we need to get points from and come tenth again."
Noble spent some time at Arsenal at the very start of his development and he has fond memories of going back to north London and winning in the 2006/07 campaign.
He added "I was at Arsenal as a young kid before I went to West Ham and they probably did develop me as a player a bit. I've won there once before during the great escape we had and who says we can't do it again?"