Robertson opened with a break of 103 to set the tone for a one-sided affair and soon followed that up with a break of 140 in frame three – the tournament’s highest break.
Runs of 36 and 80 secured the last two frames to ensure the Australian a place in the next round.
Joining Robertson in the next round is Judd Trump, who overcame Alan McManus 5-3 earlier on Thursday.
Gibraltar Open
'Like a thunderbolt' - Lisowski wows with brilliant pot
The Ace in the Pack raced into a three-frame advantage courtesy of runs of 52, 64 and 67 but McManus rallied to take the next two.
Breaks of 68 from Trump and 41 from McManus saw the pair exchange frames before Trump sealed his progress with a break of 107.
Australian Open results
Mark Davis  5 - 3 Shaun Murphy 
Neil Robertson  5 - 0 Jamie Jones 
Ricky Walden  5 - 2 Martin Gould 
Judd Trump  5 - 3 Alan McManus 
Xiao Guodong  5 - 4 Peter Ebdon 
Stuart Bingham  5 - 2 Mark Joyce 
Gibraltar Open
'An unbelievable shot' - Lisowski wows with brilliant red
Gibraltar Open
‘Oh dear!’ - Lisowski the beneficiary of ‘incredible’ fluke