If me and a group of fighters were being held captive and were only allowed to perform 5 strength training movements I feel they should be as followes:
Deadlift: Locked in an armbar or triangle choke lifting you opponent off the Mat to slam him is a valuable attribute to have. This exercise works my grip back and legs all in one motion. Bang for my buck im going deadlift.
Various Pushups: While it is the same motion, placing my hands at different angles and positions (close, wide, neutral, knuckles) I can hit and improve my chest and shoulder girdle. Adding the knuckle pushups increases my tolerance for impact and increase stability on my punches.
Rope Climbs: With legs or without, Rope climbing will increase me grip and back muscles in an extremely functional way for fighting. The pulling and instability of the rope forces you to work harder than a pullup. Using legs or without, you can vary the intensity and really push your limits.
Explosive Burpees: A combo of a sprawl, pushup and vertical jump, explosive burpees will work the whole body while taxing your aerobic and anerobic eneergy systems. They wont increase strength to the level of the first three exercises but are a great addition for an athlete. When time is of the essence and you have limited selection; to use a Burpee will aid you greatly.
Tabata Thrusters: If any person here has ever done a tabata method workout, you know the ungodly potential to break you down. Using any weight you can you continually squat and press a weight for 20 seconds, followed by 10 seconds of rest. Continue this for 8 rounds or 4 minutes. People who question this selection and have never done this workout, grab 25 lb dumbells and do as presented.
While I agree that there are better programs in the world then the one I just presented. I feel that within your restrictions you couldn't get better than this. You have max strength and total body development, along with Metabolic work, and aerobic and anerobic work development.
Any fighter who did this workout at their own max intensity (weights and reps that are challenging) Will definately put themselves in position to improve in the right ways for fighting.