It could be a linkage problem. Get under the car and see if the middle gear lever moves when the car is shifted into reverse. The rod may have come loose from the linkage or transmission lever.
The next culprit would be the reverse shift finger inside the transmission.
I believe the five speed will work but you will also need the linkage and the correct driveshaft. Expensive and hard to find.
Falls Church VA
'66 200, '66 230SL, '96 SL500. Sold: '81 380SL, '86 300E, '72 250C, '95 C220, 3 '84 280SL's '90 420SEL, '72 280SE, '73 280C, '78 280SE, '70 280SL, '77 450SL, '85 380SL, '87 560SL, '85 380SL, '72 350SL, '96 S500 Coupe