If its the original trans to the car, then you can check the sticker in the trunk for the trans code that can be looked up which will tell you what 5th gear you have as well as if it has an LSD. If it's not the original trans (likely since its a racecar), or the sticker is missing/painted over, you can crawl up underneath the trans with a mirror and get the code off the top of the transaxle where it bolts to the torque tube. The 5th gear can be swapped, however, with the trans in the car so many times that gear doesn't match the code on the top of the trans.
There is another way which allows you to measure the number of times the wheel turns vs engine revolutions that involves jacking up the rear of the car, counting wheel revolutions vs the crank, then doing some math.
The last way is just feel through driving it and lap times. Do you have any tracks which require 5th gear in Colorado? If not, then it really wasn't ever a big deal so odds are its a tall 5th.
LSD check is simple. Jack up rear of car, put in neutral, and turn a rear wheel. If both rear wheels spin the same direction it has an LSD. If they spin in opposite directions, it has an open differential.