The Hoops will travel to First Division Raith Rovers providing they win their fourth-round replay at Arbroath.
The firm have also pushed out Rangers from 10-1 to 12-1 after they were paired with Dundee Utd who are 9-1 second favourites.
William Hill make United 1-2 favourites to knock out Third Division Rangers who are 6-4.
Spokesman Paul Petrie said: “With the potential of so many all SPL ties, Celtic will be delighted to draw lower-league opposition – if they can overcome Arbroath of course.
“The draw has also opened up for those further down the betting, due to the fact that the second, third and fourth favourites have all been paired with each other.”
Dundee, who face Turriff or Morton at home, are the other big winners in the draw and have been cut from 40-1 to 25-1.
Scottish Cup outrights (McBookie.com): 8-11 Celtic, 9-1 Dundee Utd, 12-1 Hibs, Rangers, 14-1 Aberdeen, Motherwell 20-1 St Johnstone, 22-1 Kilmarnock 25-1 Dundee, St Mirren, 33-1 Inverness CT, Ross Co 40-1.
Fifth Round Draw
Raith v Celtic/Arbroath
St Mirren v C’beath/St Johnstone
Dunfermline v Dumbarton/Hamilton
Hibs v Aberdeen/Motherwell
Falkirk v Forfar
Dundee United v Rangers
Dundee v Turriff/Morton
Kilmarnock v Inverness/Ross County
Ties to be played on the weekend of February 2 and 3, 2013.