With National League big hitters Notts County, Wrexham and Chesterfield all out and holders Bromley also already fallen, it’s the most open competition for years.
BT Sport pundit Aaron McLean carried out the draw and those still standing are one game away from the quarter-finals.
Winners of the fith round matches receive £6,000, while the losers still bank a cheque for £1,750.
There are some big all National League ties as Southend United welcome York City while Eastleigh host Maidstone United, who sent Notts County packing on Sunday.
Aldershot Town face Dorking Wanderers while Altrincham will fancy their chance of a trip to Wembley - but they have to get beyond brave Bracknell Town first.
There will be Step 2 representation - Hungerford Town face Farsley Celtic for a place in the last eight.
Maidenhead United meet the winner from the Harrow Borough vs FC Halifax replay.
The ties will be played over the weekend of February 11.
The draw in full:
Hungerford Town vs Farsley Celtic
Maidenhead United vs Harrow/FC Halifax
Southend United vs York City
Eastleigh vs Maidstone United
Torquay/Taunton vs Barnet
Aldershot Town vs Dorking Wanderers
Banbury/Coalville vs Gateshead
Bracknell Town vs Altrincham