It was always going to be a testing afternoon for Gary Waddock's side and it proved to be in Shropshire.
Goals from Alex Rodman, Shaun Whalley, Stefan Payne, Arthur Gnahoua and Carlton Morris sent Shrewsbury through to the next round.
Shots boss Gary Waddock said: "It was a difficult afternoon, we knew it would be. They're sitting top of League One for a reason and they showed us why. Their finishing was clinical.
"The scoreline tells you a story. It's difficult to take. We came up here to try and make it difficult but that wasn't the case this afternoon.
"They're League One, they're looking to go into the Championship, we're in the National League looking to get out of there - there was a gulf and that showed."
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