The Group H demolition followed on from a 3-1 win in Belgrade and the 6-0 rout of Portuguese side Braga last month and their form in Europe has been in stark contrast to the weekly traumas they endure on the home front.
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With a competition record 14 goals from their first three group matches and Manchester United's mark of 20 in their sights, fans could be forgiven for wondering what all the fuss is about UEFA's blue riband competition.
Whatever the relative strengths of some of the so-called "champions" put before them so far this season, Arsenal manager Arsene Wenger was delighted by the quality of his vibrant side's attacking panache on Tuesday.
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Five different scorers was proof of the goal threat that his side possess, and even Shakhtar's late consolation was scored by Eduardo, the popular Brazilian-born Croatian who left North London for eastern Europe in June.
"When you win 1-0 people say it's too difficult and when you win 5-1 people say it's too easy," Wenger told reporters after first half goals from Alex Song and Samir Nasri laid the foundations for a thrashing completed after the break by Cesc Fabregas, Jack Wilshere and Marouane Chamakh.
"It's difficult to assess why we won 5-1. I think tonight we were intelligent able played to a very good technical level.
"The teams we play in the Champions League are used to dominating the games in their (domestic) championship so they don't come here to defend. Then when you are superior you always have the chance to score goals.
"The points were important, not the number of goals."
Arsenal's display could not have much better as they prepare for the more meaty challenge of facing title-challenging Manchester City away on Sunday.
In many ways, in the three European games they have played so far, Arsenal have proved nothing the fans did not already know.
WORLD BEATERS
Given time and space, which sides like Braga and Shakhtar offer in spades, Wenger's side look world beaters. As West Bromwich Albion proved in a 3-2 win at the Emirates last month, however, Arsenal are not the finished product.
With Fabregas back pulling the strings in midfield after a month-long injury lay-off and teenager Wilshere looking more assured with every passing game, Arsenal were a formidable force on Tuesday.
Wilshere, who was packed off on loan to Bolton Wanderers last season to gain some first-team experience, has particularly caught Wenger's eye, even if his tackling remains rash.
"Wilshere didn't hide from challenges tonight," Wenger said of the 18-year-old who was sent off against Birmingham City on Saturday for a two-footed lunge and escaped censure for a similar rush of blood on Tuesday.
"Sometimes when you get such a storm you go the other way but what is important he just played football. He is great technical player but he doesn't hide from challenges and that's something you do not want to lose."
"He can play in every position in midfield. Give him time, and let him play."
While Wilshere, whose beautifully crafted goal that made it 4-0 was the pick of
