Everything is calmer in Kharkiv and the locals are returning home, but it is still dangerous to be in the city.
In Kharkov, there is still a threat of rocket attacks on the city. And therefore, if possible, it is still better to evacuate from Kharkov to safer places. This can be done by private transport or by rail.
Ukrzaliznytsia has published a schedule of free evacuation trains from Kharkiv on May 13: