G-5 is an agent with British Intelligence.
That is just a guess on my part. He never expressly states it and towards the end of his recorded adventures he is referred to as an "international agent" but most of the operations we learn about have him working on behalf of or reporting to British Intelligence. He most definitely is at home in Europe which is the backdrop for all but one of his escapades and his obvious command of numerous European languages is extensive and impressive as is his ability to fit in to his surroundings when he feels the need.
G-5, a man whose real name is not only never spoken but who also eschews the use of aliases, preferring to use his cover designation if a name is required, is a handsome blond haired man likely in his mid-30s based on his depiction. He is in excellent shape and is more than a match for just about everyone with whom he needs to scuffle. He is quite good at boxing and knows a thing or two about the martial arts, throwing and flipping his enemies a lot.
There is no indication that G-5 has any lasting relationships, at least during the time of his activity, which is understandable since the agent gets around a great deal, surprising considering the state of hostilities around him. With such a wide range of territory, it is not surprising that he does not have a chance to put down any roots. Regarding the territory he covers, a few times he is asked/hired to head to a trouble spot to take care of a crisis brewing but even more often he is just in the right place at the wrong time (for the bad guys).