Seven-time world champion Hamilton was nearly seven tenths behind polesitter Charles Leclerc's Ferrari, and six tenths behind the Red Bull of 2021 title rival Max Verstappen, admitting that both cars are "in another league".
But despite qualifying off the front two rows, something which happened to him only once in 2021, Hamilton says he was pleased with how the team had mitigated the handling problems that appear to plague the new Mercedes W13.
After beating new team-mate George Russell by nearly a second as the former Williams driver struggled to ninth, Hamilton said: "I'm not gonna say I'm relieved.
"I'm generally really happy with today given where we've been in the last two last few weeks, the struggles that we've had, the problems we've had with the car.
"It's been a bit of a nightmare to drive but we've just kept our heads down and kept working away, so I'm proud of everyone for just staying positive.
"To get fifth in qualifying, those guys ahead of us are in another league so I'm generally happy with where we are. It's not the front row but we'll make improvements, and we'll do the best we can."
After Friday practice, Hamilton and Russell had already pointed out Red Bull and Ferrari were up to a second quicker on high fuel runs, which resigned the Brackley team to a weekend of damage limitation.
Hamilton acknowledged he wouldn't be able to compete with either team on Sunday and would instead be focused on the fight for fifth against the likes of Valtteri Bottas, his former team-mate who qualified a remarkable sixth for Alfa Romeo, or the equally surprising Haas returnee Kevin Magnussen in seventh.
"Those guys [Red Bull and Ferrari] will be going away, so we're not in the fight with those," he admitted.
"They were a second ahead of us yesterday through race pace, so my battle is with the guys behind most likely.
"Of course, I'll try to be as fast as I can and get ahead. But, as I said, their performance is quite a bit ahead of us."
