Coal ≠ energy. In an industrialized world coal has many uses, and energy is just one possible use. Coal is instrumental in the production of steel, one of the most used metal alloys on earth, and with Panem's military I bet we find it uses quite a lot of steel to support. Steel is also instrumental in large buildings that cities contain (think the capital).
While we don't have a confirmed location for District 12, it's most likely located along the northern part of the Appalachian Mountains, which puts it in a prime area to mine bituminous coal, which is the kind of coal used in industrial purposes and not in electricity production.
The bituminous coal fields of western Pennsylvania, western Maryland, southeastern Ohio, eastern Kentucky, southwestern Virginia, and West Virginia contain the sedimentary form of coal.
Steam coal - also known as thermal coal - is mainly used in power generation.
Coking coal - also known as metallurgical coal - is mainly used in steel production.
Other important uses of coal include alumina refineries, paper manufacturers, and the chemical and pharmaceutical industries. Several chemical products can be produced from the by-products of coal. Refined coal tar is used in the manufacture of chemicals, such as creosote oil, naphthalene, phenol, and benzene. Ammonia gas recovered from coke ovens is used to manufacture ammonia salts, nitric acid and agricultural fertilisers. Thousands of different products have coal or coal by-products as components: soap, aspirins, solvents, dyes, plastics and fibres, such as rayon and nylon.
Also according to the wiki (which i will attempt to get book quotes to back up) District 5 is
- the 3rd richest district
- runs approximately 15 power plants
Other than the large hydro-electric plant we see the rebels sabotage, it also has a solar plant named after President Snow, and seems to export its energy across the continent, which appears to be why District 12 (other side of the continent) has sporadically insufficient power.
Its also reasonable to assume that since district 13 had the knowledge and ability to create nuclear weapons, which is a far more indepth task then harnessing nuclear energy in a power plant, district 5 may also have been operating a number of nuclear power plants.
Some of this is referenced to thecaptiol.pn website hosted by lionsgate.
The Hunger Games Tribuite Guide, licensed by Lionsgate has this to say on district 5.
