Make them consistent, and put them in priority order. What's most important to you? Pick 3 things, and do 1 a week for 3 weeks. Only work on the one item the first week. Maybe it's not using fingers but to use a knife to push food onto the fork. Fine. Choose a couple of manageable meals, and make a game of it, sort of a challenge rather than letting him see your exasperation. Don't worry about cutting the meat yet - just work on no fingers.
Maybe next week, you do the chewing thing. "Let's do 20 chews and a swallow before talking! Let's see who can do it the longest without showing what's in their mouths!" Then praise praise praise. It's so much nicer, it's so much easier to understand you, etc.
Week 3, do the elbows. Do NOTHING else during this time - no setting the table, no clearing the place (unless those skills are already mastered), no napkin reminders, etc. Do not mention one single faux pas you want him to work on besides the weeks' focus.
After 3 weeks, take a break. Don't introduce any new skills right now. Otherwise you'll overwhelm him with 52 new things during the year.
Then at the end of the 3 weeks, reward him with a family meal out at the place of his choosing (no pizza and finger-food places though!).
There are videos and manners programs too - I have a friend who teaches them to kids of varying ages. See if the library can acquire something for you to borrow - you may get some great ideas. Sometimes learning how to set a table, what goes where (and why) is interesting too. Calling attention to what the utensils are and where they belong can help some kids make order out of a chaotic table setting! You can set the table part of the way and then see if he can help you find what's missing.
Some families like to give their kids their own kid-friendly utensils. That can have a benefit in that they feel special - but it can be more difficult when they go out and get an adult-sized knife. Your call.
Beyond that, a good way to get kids to step up is to say that certain privileges are for "big kids" who are old enough to use a knife, chew their food before speaking, keep their elbows off the table. So if they want to try new challenges and events, they have to be trustworthy in their behavior and manners.
When my husband's kids were older than yours, we really had had it with their lack of manners. It was harder because they were transitioning from one house to the other, and they tended to see Daddy's house as Party Time. Which it wasn't. One time, we switched up the dining room - we sat in their usual seats, and put them in our seats. And we proceeded to eat like each of them - we took a whole stick of butter to put on the vegetables (as one kid habitually did), and we ate green beans the way the other one did (pushing it in with one finger). And yes, we talked with food in our mouths. They got the point. We also left them with the dishes and the leftovers to put away since they were the "grown-ups" and we were the kids - we bolted from the table to the TV and ignored them. It was dramatic but it worked. It's not for everyone and probably not for a 5 year old, but it's an option!
Good luck!