I am a slim male, mid 30's and I have a big belly. Are there any specific exercises I could do at home that would target that area?

Well, no. . There are no specific exercises to reduce your belly. Even though you are slim, if you have a large belly, that means you have a lot of intraabdominal fat, which is particularly unhealthy. A sensible fat reducing diet that is fairly high in protein (to help you build muscle) coupled with lots of exercise should decrease fat overall and increase muscle.
Maybe, but... Once you've ruled out abdominal wall hernia, the only way to effectively spot-reduce unwanted abdominal tissue is to surgically remove it. The "pear" body type preferentially stores fat around hips; "apples" store it around their waist. Lose 1 pound of fat for every 3500 calories you drop or exercise off, but you can't pick where--sorry. Abdominal exercise will improve tone of existing muscles.