I'm Jack with the openFDA team. Based on hitting the 5100 result limit I can surmise that you've already discovered the skip limit. What isn't reflected in our current documentation because it's a brand new change is that the skip limit has now increased to 25,000. You can find out all of the details of the search criteria here. If you're looking to explore larger chunks of data than 25,000 or want more advanced querying options than our API provides, we do host all of the data for direct download. There's more information on downloading the data available here.
Let me know if you have any other questions.