We report on five binary pulsars discovered in the Parkes multibeam Galactic plane survey . All of the pulsars are old , with characteristic ages 1–11 \times 10 ^ { 9 } yr , and have relatively small inferred magnetic fields , 5–90 \times 10 ^ { 8 } G. The orbital periods range from 1.3 to 15 days . As a group these objects differ from the usual low-mass binary pulsars ( LMBPs ) : their spin periods of 9–88 ms are relatively long ; their companion masses , 0.2–1.1 M _ { \odot } , are , in at least some cases , suggestive of CO or more massive white dwarfs ; and some of the orbital eccentricities , 10 ^ { -5 } \lesssim e \lesssim 0.002 , are unexpectedly large . We argue that these observed characteristics reflect binary evolution that is significantly different from that of LMBPs . We also note that intermediate-mass binary pulsars apparently have a smaller scale-height than LMBPs .