The first place I would look is at the timing, a vacuum leak will also have this effect on an engine.
NO it would not.
The transmission doesn't lose power, but it quits getting power if the clutch starts slipping. Without going into detail about the physics of a clutch, the most energy is being transferred through the clutch when in the highest gear thus it is fifth gear where slipping is first noticed. My guess is its time for a new clutch.
my truck lost power also i had bad battery cables
change the fuel filter
Most likely a dead battery.
applying pressure to the brake pedal
You could either be in too high of gear or your (if manual)clutch might be going out.
Any engine will lose RPM going up a hill, its called gravity and the engine has to overcome it. The heavier the vehicle the more RPM you lose. Thats also why transmissions have all the extra gears. Lower gear equals more pulling power and less speed, higher gear is less pulling power and more speed.
might be trans Catalytic Converter stopped up/broken apart Timing off Plug wires out of order on the cap
check and clean the battery terminals
Belt
Plugged fuel filter, plugged air filter, restricted exhaust, plugged catalytic converter.