  The multipocket Fermi surfaces of iron-based superconductors promote pairing
states with both s_{+-}-wave and d_{x^2-y^2}-wave symmetry. We argue that the
competition between these two order parameters could lead to a
time-reversal-symmetry breaking state with s+id-pairing symmetry in the
iron-based superconductors, and propose serveral scenarios in which this phase
may be found. To understand the emergence of such a pairing state on a more
rigorous footing, we start from a microscopic 5-orbital description
representative for the pnictides. Using a combined approach of functional
renormalization group and mean-field analysis, we identify the microscopic
parameters of the s+id-pairing state. There, we find the most promising region
for s+id-pairing in the electron doped regime with an enhanced pnictogen
height.
