No need for branches, see comment above demonstrating sltu.

For a long carry chain, I guess it might look like this:

  ; Inputs: x = 4-word number, in a3:a2:a1:a0,
  ;         y = 1-word number, in a4.
  ; Output: x+y, 5-word number, in a4:a3:a2:a1:a0.
  add  a0, a0, a4
  sltu a4, a0, a4 ; a4 = carry bit
  add a1, a1, a4
  sltu a4, a1, a4 ; a4 = carry bit again
  add a2, a2, a4
  sltu a4, a2, a4
  add a3, a3, a4
  sltu a4, a3, a4