No. "I've known him since 2005." As a rule of thumb, you use (verb)ing if you can actually see the action. Stative verbs such as "to know someone" don't take the (verb)ing form.

No, "I have been knowing him since 2005" is not correct. You have to say here "I have known him since 2005". However, you can use other "stative" verbs with the -ing form in many cases, but this is not one of them. Here are just a few examples of where you CAN use these verbs in this manner: 1. I have been HOPING to meet you for a long time. 2. I have been THINKING about this situation for months. 3. I have been FEELING sick since Thursday. 4. I have been LOVING this job ever since I started working here. 5. I have been HATING this job since John became my boss. 6. I have been BELIEVING his lies for too long. 7. I have been DOUBTING his lies for a long time.

Here is a list of stative verbs to help you out. :) http://www.perfect-english-grammar.com/support-files/stative-verbs-list.pdf