The German finished behind the Red Bull and Ferrari pairings as he went on to capture his best finish of the season.
Hulkenberg, who slumped to 13th last time out in Belgium, is delighted with his team after putting in a strong performance at Monza.
"It's a great result - another great performance by the team today," Hulkenberg told reporters. "Fifth was probably the right result for us - we only finished behind Red Bull and Ferrari, which was great.
"Despite starting third, it was always clear keeping the Ferrari and Red Bulls behind was not realistic.
"I lost two places right at the start, but then the pace was good and, especially towards the end, I was able to catch up quite a bit again. I kept the Mercedes behind with Nico leaving no room for me making any mistakes."
Hulkenberg sits 14th in the drivers' standings.