Question about filling void between outer wall and drywall

[gradygodfrey]

Hello,

I have a gap of about 40x5 inches between the outer wall of my house and the drywall inside. I'd like to block it up as we're in that time of year when mice may crawl in and get in the house. The filler foam was unsuccessful, so I was thinking of blocking it up with some wood and then using filler foam around any gaps to truly seal it up.

Would this be the beat course of action, or am I missing something better? Would getting some insulation cut to fit be a better solution, or something else? 

Thanks in advance!