O GNU sort
com a opção -g(--general-numeric-sort)
deve ser capaz de fazer o truque
sort -k5,5g -t '_' <<!
beginning_num1_734_num2_1.363e+12_num3_800.pdf
beginning_num1_735_num2_7.453e+13_num3_800.pdf
beginning_num1_1007_num2_9.453e+12_num3_1200.pdf
!
beginning_num1_734_num2_1.363e+12_num3_800.pdf
beginning_num1_1007_num2_9.453e+12_num3_1200.pdf
beginning_num1_735_num2_7.453e+13_num3_800.pdf