My stepdaughter's son was like this, and I have to say that, the older and bigger he got, the more malnourished and moody he got. He was eating enough quantity, but not enough variety. So I commend you for working to take a look at this. My friend is a kindergarten teacher and sees more and more behavioral & focus issues with kids the more junk they eat and the pickier they are.
For starters, you can switch to really healthy alternatives of the foods he eats. You can make your own chicken nuggets with white meat chicken and a breading of wheat germ and ground flax seed (you can find it in the grocery store marked as ground flax seed or flax meal). Dip the chicken in egg and then in the breading, fry up in canola or olive oil until crispy on both sides, then finish in the oven. This gives healthy fats and no salt, although if you have to add a little salt for flavor, it's not the end of the world. Then you can switch the pasta and rice to whole grain pasta and brown rice. Even if you have to go half & half to start, that's fine.
You can look into cookbooks such as Sneaky Chef and Deceptively Delicious - the libraries will have them. My son was a horrendous eater - we joked that he only ate "tan food" - PB, nuggets, crackers, fries. We couldn't even get him to eat at McDonald's although I felt guilty about even pushing him to do this! We did all kinds of sneaky things (before these cookbooks came out!) like putting soy powder in the batter and going for really healthy breads. I made pancakes with added wheat germ and oatmeal and soy milk. When my husband and I would make steamed vegetables, we saved the water in the bottom of the pot and used it for rice or couscous - no sense wasting those vitamins. That nice "green water" was fully absorbed in the rice our son ate. He also ate zucchini bread and banana bread. Kids also like to dip foods - raw veggies in ranch dressing, or in hummus, can be fun as well as healthy.
You also can continue to offer a variety of foods with meals, and you should. Research shows that kids need to try a new food at least 6-8 times before acquiring a taste for it. Don't offer him large quantities of the foods he loves - offer a little and offer some additional alternatives. A child of 5 will not starve if he misses a meal or two. You need to be firm about loving him and caring about him and making sure he knows that this is the reason you are expanding his diet. I would steer away from restaurants at this point - let him get the variety at your house rather than take a chance on an unfamiliar place. Offer foods, and try to get him to try them. If he is "done", then take the plates away and announce that dinner is over and it's time for story or bath or whatever. If he is still hungry, put the same food out again! That's dinner! It can also be breakfast the next day.
So, you have to strike a balance between giving him the foods that he wants, making healthier versions of the foods that he likes, and introducing new foods either directly or in hidden form. The key is NOT to make mealtime a battleground - you have to try (I know it's hard) to take your emotions out of it and not engage in any of his tantrums or drama. Be matter of fact and balanced.
I would also take away any purely junk food at this point until you get more balanced nutrition in him. Cut back on the juices if they are filling him up with too much sugar.
Lastly, consider an outstanding nutritional supplement which can be put in the many of the liquids he drinks. It's made by the same scientist who came up with ProSoBee infant formula and who is world renowned in the area of pediatric liquid nutrition. It's called Now for Kids and it's a whole food, contains vitamins and minerals and trace elements that we don't get from our food anymore (even if we eat perfectly), and it also has key elements like omega 3s and DHA which are essential for healthy brain development. It's made here in the US under strict standards, and it's an incredible bargain when you consider that it is so highly absorbable that nothing is wasted. It's available through distributors who will give you great support and help. Contact me for more info if you like. You will see a huge difference in your child with immediate nutrition while you continue to try to introduce new foods. He'll be more agreeable once he's better nourished with things his body craves. I've seen tremendous changes in our family and want to pay it forward by helping others.