Probably the most efficient design would be a Switch Mode adjustable power supply [SMPS]/LM338 hybrid. The SMPS would track the LM338 such that the LM338 maintains a minimum dropout voltage [the main source of inefficiency since the LM338, a linear regulator, must dissipate the power produced by the current it is delivering times the dropout voltage. Worst case is when the LM338 is adjusted down to 1.2V (and running at 5A) whence it must dissipate something like (32.8V-1.2V)*5A = 159W! (assuming best case input voltage of 32.8V - because ~2.8V is the worst case dropout voltage, according to the TI datasheet). If, instead, a SMPS supplies 4V to the LM338, it will only have to dissipate (4-1.2) * 5A = 14W.
