Is it permissible to perform five prayers with a single ablution, and what is the ruling concerning one who states that the Messenger of Allah (peace and blessings be upon him) performed five prayers with a single ablution, out of fear of lying about the Messenger of Allah (peace and blessings be upon him)?

The Messenger of Allah, Allah's peace and blessings be upon him, performed the five daily prayers with a single ablution during the year of the Conquest. His practice was to renew ablution for each prayer, but it is not obligatory to perform ablution for prayer if a Muslim is already in a state of ablution. This is what Muslim scholars have agreed upon. As for unintentional error in transmitting a hadith, it is not considered a lie. It is clear that the questioner is suffering from obsessive thoughts, and the best treatment for her, after seeking Allah's help, is to turn away from them and pay them no mind.