WORD 'slow' has a SPECIFIC meaning with respect to time.It refers to (of a clock or watch) showing a time earlier than the correct time.This means that the watch shows a time five minutes before the actual time. Lately' is an adverb that refers to something recently. Also lately is used for states or for repeated EVENTS, mostly with the present perfect tense.This sentence does not use a present perfect tense nor does it REFER to any recent event.Also, the word 'past' cannot be used, as it does not have a referent as to 'what time has the watch passed.'In the CASE of 'late,' it is unusual for a watch to 'be late' rather it should preferably be called 'slow.' Therefore, the sentence is: My watch is five minutes slow.