Is vowing to fast five days when traveling with a mahram for study, a vow made during ablution and marred by misgivings, considered a binding vow or merely a self-thought?

"Self-talk about vowing to fast certain days, without uttering it verbally, does not entail a ruling. This is because a vow requires a specific formulation that the one making the vow articulates with their tongue. The Messenger of Allah, peace and blessings be upon him, said: 'Indeed, Allah has forgiven my Ummah for whatever crosses their minds or whatever they whisper to themselves, as long as they do not act upon it or speak about it.' The consideration is based on verbal existence in verbal matters and practical existence in practical matters."