Without a contract do I still owe back money?

When I was hired at my job it was told to me that they would pay for me to receive outside training that I needed for my license. At the time when the training began, they approached me with the idea of having to pay the money back if I did not stay at my job for 5 years. There was an email exchange which ended with us both signing the email and a final email that a contract would be drafted up. The contract was never drafted and I was told verbally that they were unable to get this contracted drafted. I left my job prior to the 5 years and they are now sending me letters requesting this money. There is still no contract or no invoice. The money was paid in forms of bonus’s in my pay check. Am I legally obligated to pay this?