How do restaurants make chicken fried rice? What ingredient am I missing?
For me it isn't fried rice without toasted sesame oil, and the fried rice I have had in restaurants always tastes to me as if it contains toasted sesame oil. Peas are pretty required too. BTW, La Choy is synthetic soy sauce, it was at the very bottom of the America's Test Kitchen taste testing of soy sauce (sorry, paywalled), the only soy sauce to get a "not recommended" rating. Use anything but that. From that taste test: "In summary, could this be any worse?"

I actually fry the rice in toasted sesame oil, but I have reason to believe that some toasted sesame oils will burn at that temperature. To experiment with that is on my list of things to do. So I can only say that this sesame oil has a high enough smoke point to fry rice.

For whatever reason, the label does not say that this sesame oil is toasted. It is, and it's a very high quality oil.

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EDIT: In other answers, Pepi mentions ginger, and Teresa mentions oyster sauce. I second both of those. I always use ginger and garlic and either oyster sauce or hoisin sauce. Also, Cindy mentions salt, the eggs do need salt. I actually use all of these in my rice (which looks like this when it is done, this is mine):



I'm assuming already cooked meat, peas sitting in a colander defrosting, water run over them enough to rinse off any clinging ice, and day-old rice.

I start by making slightly underdone scrambled eggs, seasoned just like I season eggs that I'm eating for breakfast. I set the eggs aside on a plate and wipe out the skillet (or flat bottomed wok) with a paper towel, and let it get pretty hot. I don't attempt to use extreme heat, the same level of heat I'd use to sear chicken works fine for me.

I add a good pour of the sesame oil, perhaps 1.5 tablespoons for two big servings (like the amount of fried rice in the picture above), let it heat for 30 seconds or so, then add ginger and garlic and stir. Then I add whatever veggies I'm using in the order of how long I want them to cook (all veggies except peas). When the veggies are just about fully cooked to to the level I want them in the rice, I add the rice, breaking it up and stirring in the veggies. I lightly press everything into the bottom of the pan, then I don"t touch it for a few minutes. I want the rice to get a bit of a brown crust along the bottom and to get mostly heated through before stirring again. This adds color and flavor, and helps keep the rice from sticking. This step seems to bridge the flavor gap between the the rice made with the super-high-heat that Asian restaurants can achieve, and the more moderate heat of a typical home stove. 

In the meantime I mix my sauce. The proportions are up to taste, I usually go about half and half soy sauce and hoisin or oyster sauce. Less soy if is is dark, more if it is light or reduced sodium. I'll usually make just shy of a cup of sauce, knowing I won't use it all.

When the rice has formed a crust, I stir in the meat. Then the sauce, a bit at a time, tasting as I go. Finally I stir in the peas and eggs. I garnish with some chopped cilantro on the plate. Voila.

You mention Five Spice. That would be interesting, and possibly very good, but it is not a flavor that I associate with fried rice.