Non-league is low level but he scored enough goals to bring him to Leicester's attention and yes, his record at Leicester is as you say. He has had 2 seasons in the Championship and 2 in the Premier League.
In both pairs he struggled in his first season and did better in his second as he got used to the new level.
I do think last year was probably his best ever year, I doubt he'll top it, but over his whole career he's scored goals.
You wouldn't expect a player from the non-league to come straight into the top leagues and be scoring at the same rate but his speed of improvement gives signs for hope that he'll get a reasonable number of goals over the next few years.
His record is scoring goals at every level he's played at, including international level recently. If you look at the record of any striker playing at a new level - usually this would be at a young age - then there will generally be some poor seasons and then improvement, that's what we see with Vardy.
And the period of adjustment argument doesn't meant he'll get 5 goals for us, what kind of reasoning is that? I didn't say anything about a new club, it was a step up in level. We are in the same league as Leicester.