If that is indeed the case, and each primary winding is wound for 220V and the secondary will output 120/240V then I would first bench test the xfmr. Good chance the voltage at his service electrical panel is 240V to 246V. What will be the output of the xfmr? Above 124V ain't good.....
The electrician is right.
But just to add there are two 120V secondary windings.
Each winding is good for 2.5 KVA each.
Say the electrician was not instructed by Dangelod how he wanted the secondary output of the xfmr configured and the electrician installed the xfmr and new panel and wired the xfmr and panel for 120/240V.
Dangelod may have told the electrician he wanted all 4 branch circuits wired from the same leg of the panel and not from both.
In that case the loads connected to just one leg to neutral would be only connected to one 2500Va winding of the transformer.
So to get the full rating of the transformer both secondary windings must be connected in parallel (120V out), same for both primary windings must be conned in parallel, (if as Ngjockey has indicated dual windings 220/440V), to get the full 5 KVA rating.