David Moyes has set his struggling squad the win target ahead of Sunderland’s return to Premier League action against Burnley on Saturday.
Skipper O’Shea agrees with his manager that the Black Cats, six points adrift, would have a fighting chance of staying up if they string together those wins.
But having recently taken a trip down memory lane, he knows Sunderland may have to set their sights even higher.
“If we win those five games as the manager says we’ll give ourselves a chance,” said O’Shea.
“It might not be enough, you could win six, seven it might not be enough.
“I was watching the Premier League Years a few days ago and remember some of the teams, the runs they went on to try and stay in it and were so unlucky.
“Some years it’s worked for us, some years it’s worked for other teams,” added O’Shea who knows pulling off another great escape is not inevitable.
Basement side Sunderland do, though, still have five of the bottom seven teams to play and O’Shea says ultimately the club’s fate remains in their own hands.
“Ultimately, as we know ourselves from the last few years, if we do our own job, that takes care of it,” he said recently.
O’Shea, who has won 116 caps, has been included in Martin O’Neill’s 39-man provisional Republic of Ireland squad ahead of the upcoming international break, alongside January signing Darron Gibson.
Gibson’s call-up ends a ten-month international exile for the midfielder, who had his hopes of appearing in last summer’s European Championships dashed because of a lack of game time.
The 29-year-old joined Sunderland from Everton in January and he has made four appearances since teaming up with Moyes at the Stadium of Light.
The central midfielder will be looking to add to his 29 international caps.
Currently unbeaten after four games in their World Cup qualifiers, Ireland sit at the top of Group D, having won three and drawn the other.
The Republic play Euro 2016 semi-finalists Wales at the Aviva Stadium on Friday, March 24 in the upcoming international break, which takes place after this weekend’s round of Premier League games.
O’Neill’s side then face a friendly against Iceland.