It depends on the rest of the sentence. Take out the words "Jimmy and I" and say the sentence using both 'me' and 'I'. Which makes sense? For example, let's say the sentence is, "Jimmy and I went to...
Jimmy Rogers was born on June 3, 1924 and died on December 19, 1997. Jimmy Rogers would have been 73 years old at the time of death or 87 years old today.