2002 Ford Taurus won't start for several minutes after driving then stopping

What is your question?

When I drive my Taurus short distances to the store it's usually fine but still sometimes after I drive it 5 miles then leave it for several minutes it won't start until 5-10 minutes after I tried it once. It seems like the longer I let it sit after stopping the better chance I'll have at not having it start. If I let it sit over night it always starts right away. It doesn't click when I start it, it just won't turn over. It also likes to turn itself off after letting it sit idle for several minutes and it likes to die at stop lights but not very often at all. Any help would be appreciated, thank you.

What makes this problem better or worse?

The quicker I start it after turning it off the better

How long has your 2002 Ford Taurus had this problem?

Years