In this article we study spontaneous chiral symmetry breaking for quark matter in the background of static and homogeneous parallel electric field E and magnetic field B. We use a Nambu-JonaLasinio model with a local kernel interaction to compute the relevant quantities to describe chiral symmetry breaking at finite temperature for a wide range of E and B. We study the effect of this background on inverse catalysis of chiral symmetry breaking for E and B of the same order of magnitude. We then focus on the effect of equilibration of chiral density, n5, produced dynamically by axial anomaly on the critical temperature. The equilibration of n5, a consequence of chirality flipping processes in the thermal bath, allows for the introduction of the chiral chemical potential, µ5, which is computed self-consistently as a function of temperature and field strength by coupling the number equation to the gap equation, and solving the two within an expansion in E/T 2 , B/T 2 and µ 2 5 /T 2 . We find that even if chirality is produced and equilibrates within a relaxation time τM , it does not change drastically the thermodynamics, with particular reference to the inverse catalysis induced by the external fields, as long as the average µ5 at equilibrium is not too large.