I am not old enough to have seen this series during its original run, I came across it while wandering round the internet looking for old TV programmes. The Internet Archive has preserved six out of the 16 episodes, with variable sound and picture quality, but I think they are enough to give a good overall impression of what the series was like.
It stars David Hedison and Luciana. Paluzzi. Hedison plays Victor Sebastian, a CIA agent with the code name Five Fingers. He has a cover job as a theatrical agent whose company has offices in London, Paris and New York. This gives him a plausible excuse to travel in both continents while he carries out counterespionage work. On occasion he works as a double agent, appearing to act on behalf of The Party (presumably the Russian Communist Party, though the country isn't named in the episodes i saw) such as in the episode The Unknown Town.
Paluzzi plays Sabine Genet, one of his clients, a singer for whom he arranges concert bookings and she later becomes his girlfriend. She knows nothing about his second job. This gives her a number of comic scenes where he has to interrupt or cancel their dates to carry out his counterespionage work, to her great annoyance, and he tells her poorly improvised lies to try to explain his absences. Paluzzi has the less substantial role and her character is presented as naive and a little capricious. However in the episode Dossier she is persuaded by another agent to agree to undertake to make it possible for Sebastian to get into an enemy agent's well guarded mansion, though still without knowing why he wants to do so. She pulls this off with perfect confidence. And it seems at some point in the series she becomes aware of his work because in the episode The Judas Goat she is officially employed to help Sebastian with an assignment..
The series is well made with tight scripts, well paced action, lots of suspense and enough plot twists to keep the viewer guessing how each story will turn out. The acting is also consistently good and the guest characters get good enough dialogue and characterisation to make them memorable.
I do not know why this series was not continued for longer, it is very entertaining and well made for its time. What I have read about it indicates that it might have lost in the ratings competition.because it was scheduled at the same time as a more popular rival series. Pity.