25-year-old Connor Sturgeon -- who has since been ID'd as the one who shot and killed 5 people Monday in a bank -- had a history of serious injuries that he suffered while playing football ... this according to one of his ex-classmates, who talked to Daily Beast.

The former peer says Sturgeon was out of football for most of the year during 8th grade due to multiple concussions ... adding, "Then he had a couple more in high school. I’m not saying it’s the cause but I always think back to that. There were times I’d wonder, will this catch up with him? But never in this way. He’s the last person I'd expect would do this."

As a result of the concussions he suffered ... Sturgeon went on to wear protective headgear during sports he'd compete in during high school. By most accounts, he was a star -- playing on the Varsity basketball team and even running track. He was also supposedly popular.

There's an essay, unearthed from his college days as well in which he says he dealt with low self-esteem throughout his life and had hopes of bettering himself as he aged. Sturgeon wrote, "Making friends has never been especially easy, so I have more experience than most in operating alone." He also said he continues to "battle against myself."

Sturgeon worked at the bank. He's reported to have used a rifle to open fire on a crowd of people inside, which included police officers too. Sturgeon was ultimately shot and killed.