Yes, 4th gear will cause the engine to run at a higher RPM, using more fuel.
No, 3,000 RPM at 70 in 5th is not normal, it is too high. I would surmise that your transmission is not shifting into 5th or is slipping in some way and that you may indeed have a trans problem, which could be anything from low fluid level, faulty solenoids or valve body.
If you have SST, have you tried shifting through all 5 gears manually?
In any case, you should start thinking about having your transmission looked at by a professional.