I have several box sets in my collection. Going back through my library I found a supplimentary set of rules that list the five phase game turn. The rules are found in the First Edition of the Star Trek III Starship Combat Game. The Second Edition has the same art on the box, but is listed as Star Trek III Starship Combat Role Playing Game. The box that came after that was the Star Trek Starship Tactical Combat Simulator. Both the Second Edition and the Combat Simulator books list the three phase game turn and seem to have dropped the five phase option.
The rules that came with the Star Trek III Starship Combat Game First Edition set is actually a series of four simple booklets with no covers on them:
-Introduction To Starship Combat
-Book One: Basic Starship Combat (this is the one that lists the five phase game turn)
-Book Two: Advanced and Expert Rules (This is where Gorn found his Limited Fire Optional Rule. Page 6 bottom left)
-Book Three: Starship Data and Combat Charts
The Star Trek III Starship Combat Roleplaying Game, or the Second Edition, does away with both the five phase game turn AND the Limited Fire Optional rule. It does add the Command And Control RPG aspect of the game though with the addition of the larger sheets meant for individuals to take charge of a particular job on the ship. Both First and Second Editions also give the option of using a system calle TAC, which divided the important elements of the game like power generation, movement points, power to arm, shield power and damage by a factor of three. They also privided a smaller, easier to use ship sheet that allowed the use of the counters in this scale.
The Star Trek Starship Tactical Combat Simulator drops the TAC option in addition to the five phase turn and the Limited Fire Optional Rule. It does add more stuff, especially on the RPG combat end, but it isn't much different than the STIII-SCRPG Second Edition.
Of course, others have added and modified rules to fit their style of play or interpretation of what was seen on TV to make the game fit better, but sometimes house rules get mistaken for actual rules. I hope this clears up any confusion on this matter.
theSwede