Scottish Cup draw: Celtic host Partick Thistle, Aberdeen meet Dundee United
Scottish Cup holders Celtic will host Glasgow rivals Partick Thistle in the fifth round after Sunday's draw.
Hearts are rewarded for their victory over Hibernian with a home tie against Albion Rovers or St Johnstone.
Aberdeen meet Dundee United, while Highland League side Brora Rangers travel to take on Kilmarnock.
Rangers will travel to Ayr United if they beat Highland League Fraserburgh in their rearranged tie after this weekend's game was called off.
There is a third potential all-Premiership tie if Dundee can overcome Inverness Caledonian Thistle in their replay, with the winner at home to Motherwell.
The draw took place immediately after Hearts' win at Tynecastle and, although manager Craig Levein was happy to have been drawn at home, he conceded the draw was not one he would have hand-picked.
"If you asked me to pick a tie out of the hat, it wouldn't be that one," he said of the prospect of playing their Premiership rivals from Perth.
"St Johnstone I would imagine should win that game. Our record against St Johnstone recently has not been great.
"One thing I'm thrilled about is that the game is at home. We've got a good thing here just now."
Brora reached the fifth round for the first time in their history after a 1-0 win away to East Fife - the second time they have travelled to defeat a League One side this season after overcoming Stranraer in the previous round.
The side sitting seventh in the Highland League have yet to concede a goal in this season's competition and chairman William Powrie is thrilled to have been handed a fifth-round trip to Kilmarnock.
"That's what we really needed - a 500-mile trip to add to our ever increasing carbon footprint," he said.
"Seriously, we are absolutely delighted to be facing a top-flight team and we're really looking forward to it.
"We go, as we have in all the games, as the underdogs, but the Highland League is a better standard than a lot of people give it credit for.
"We will travel in hope rather than expectation and thoroughly enjoy the experience."
League leaders Celtic and second bottom Thistle come out the hat together three days before facing one another in the Premiership at Firhill.
Scottish Cup fifth round draw
Formartine United/Cove Rangers v Livingston/Falkirk
Greenock Morton v Peterhead/Dumbarton
Heart of Midlothian v Albion Rovers/St Johnstone
Kilmarnock v Brora Rangers
Ayr United v Fraserburgh/Rangers
Aberdeen v Dundee United
Dundee/Inverness Caledonian Thistle v Motherwell
Celtic v Partick Thistle
The ties will be played on the weekend of 10/11 February.