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The Imps have reached the last 16 for the first time in 130 years.
Victory on Saturday would see them become the first non-league team to reach the quarter-finals since 1925.
"If we're realistic, we'd probably only beat them once in a hundred times but we've got to believe this is that one game," boss Danny Cowley said.
"We're going to be brave, we're going to fight and give it one hell of a go. If we do all of those things, we might give ourselves that chance.
"We've achieved the impossible to get here, we've just got to go and do it again."
Lincoln beat League One side Oldham and Championship teams Ipswich and Brighton to become the third non-league team to reach the fifth round since the turn of the century, after Crawley Town in 2010-11 and Luton Town in 2012-13.
Cowley, whose assistant at Lincoln is his brother Nicky, said that the competition had "fast-tracked our development."
"It's been brilliant and whenever this cup run ends, we will cherish what we have learned from it," he added. "It will hold us in really good stead for all of our futures."
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It's not too late to enter this year's FA People's Cup - as long as you do it by the deadline anyway - and that is at midnight on Sunday.
Entry is completely FREE, there are categories for everyone AND you can enter either as a team or an individual player.
Find out all the details here.
National League leaders Lincoln City will aim to "achieve the impossible" against Premier League side Burnley in the FA Cup fifth round.