The mirror Thermodynamic Bethe Ansatz (TBA) approach offers a tool
to investigate the spectrum of AdS/CFT in the planar limit.
The TBA equations governing the spectrum are based on several
conjectures this is why it is important to test them carefully.
In this talk we will focus on the analytical
tests of the AdS/CFT TBA system in the weak coupling limit
and show that the 5-loop anomalous dimensions of the twist-2
operators of the sl(2) sector derived from the TBA equations agree
with the results obtained previously from the generalized Luscher formulae.