Is the wife divorced if the husband swore an oath of divorce that he would divorce her if he did not say the opening Takbir (Takbirat al-Ihram) in prayer within five seconds, and he was unable to do so due to scrupulousness (waswas)?

What we understand from your question is that you made your wife's divorce conditional on your not saying the Takbir for prayer within five seconds, and that you were unable to say the Takbir because you were overwhelmed by waswas (obsessive whispers). If this is the case, then your divorce has not occurred, according to the preponderant opinion regarding someone who fails to fulfill an oath unintentionally. The Malikis have stipulated that one who makes an oath does not violate it in such circumstances.