It was the first time City had scored five goals since their move to the Walkers Stadium in 2002. It was also the Foxes' biggest win since they beat Sunderland 5-2 at Filbert Street in March 2000 when Stan Collymore scored three goals and Emile Heskey two.
Pearson said: "Paul Gallagher has had a bit of criticism so it's good for him to be able to walk off with the match ball.
"He will be a player who will be important for this club for the next few years."
Pearson remained downbeat about the emphatic win.
He added: "This is a tough league and that's why I'm not going to get carried away by a good win and I'm not going to get too down when we lose."
But he was pleased the Foxes remain on course for a play-off berth, saying: "We are in a decent position at the moment but whether we remain there we will have to see.
"At some stage we may drop out of the top six, but our main aim is to be in the play-off shake-up at the end of the season."
Michael Morrison scored Leicester's first when he headed home Martyn Waghorn's inswinging corner in the sixth minute.
And Leicester doubled their lead on 16 minutes when Matt Oakley and Lloyd Dyer combined to set up Gallagher who scored with an 18-yard shot which deflected off Scunthorpe defender Marcus Williams.
Leicester put the game beyond the visitors with a third goal on 25 minutes when Gallagher curled a 28-yard free-kick around the defensive wall and inside Scunthorpe keeper Joe Murphy's far post.
And it was four for Leicester on 34 minutes when a half-cleared Gallagher cross fell to Waghorn who had time to control the ball before lashing it home from 10 yards.
Scunthorpe pulled a goal back on 55 minutes when Sam Togwell helped on Paul Hayes' goalbound shot.
Gallagher scored his third and Leicester's fifth on 75 minutes when from a deep ball by Richie Wellens he looped a clever back-header over the advancing keeper.
Scunthorpe manager Nigel Adkins explained why he made no changes to his side at half-time when they were 4-0 down.
He said: "In the first half we got a real mauling. I decided to keep the same 11 on the pitch because I knew it would hurt them and wanted to make sure that they never wanted to have that feeling again.
"I didn't want to give anyone the easy option of coming off at half time and hiding away.
"I want this to be a wake-up call for the players. I know the result has hurt them but I now hope we can go on to better things."
And Adkins admitted he had been pained by his side's sorry performance.
He said: "It's not nice to have to stand on the sidelines and watch your team perform like that.
"But you take the plaudits when things go right and then you have to take the stick when things don't go your way."