Im using tweepy to search for a keyword in all tweets in the last 5 minutes. But I couldn't find a way to do this. I saw the since_id and max_id arguments, but they only work if I know the tweet_id before 5 minutes.
There is no specific GETfeature that would allow that.
What you'll need to do is create a search for that keyword and Get search/tweets and use the since_id and max_id like you have and look at time_created_at from the JSON and filter yet again using that. 
The problem with the previous step is that you're limited to 180 tweets /15 minutes. Another solution is to use the streaming API since it'll give you recent information most are within 5 minutes and you'll be able to filter by keywords as well.
Using tweepy: how to retrieve all tweets within past 5 minutes