Hawks will now play host to Heriot's in Round 6.
Former Glasgow pros Gordon Bulloch and Guy Perret helped West Of Scotland to a 25-13 win over Hillhead-Jordanhill at Hughenden. West now face a trip to Kelso who saw off Borders rivals Gala.
National Cup Round 5
Glasgow Hawks 84 - Berwick 0
Haddington 7 - Dundee High FP 39
Hawick 29 - GHA 12
Hillhead-Jordanhill 13 - West Of Scotland 25
Jedforest 19 - Cartha QP 25
Kelso 24 - GALA 7
Stirling County 64 - Kirkcaldy 8
National Cup Round 6
Boroughmuir 48 - Selkirk 20
Dunfermiline 22 - Stewart's Melville 23