can I increase the frequency of email push on my iphone?

Nope. "Push" should do it automatically. "Fetch New Data" can only be used in up to 15-minute intervals. But I think you are talking about Push.

15 minutes is the most frequent setting, but Mail also fetches each time you use it. Fetching more often would kill your battery.

I hope they will be adding the every 5 mins option soon. I was happy with my old Samsung Galaxy Mini as it helped me stay on top of my personal and work mails. Mails just came in almost as soon as it was sent since I had it set to every 5 minutes. I decided to get an additional phone since the battery was going kaput and sometimes the screen went out. Heard raves about the iPhones so I got the iphone5. I noticed that I did not see new mails unless I checked the mailbox and I had to wait. It frustrates me to find that this new it phone can of put me on top of important things. I need to see my mails all the time as I usually have important and urgent matters throughout the day. I checked again in settings and in the net only to find that the most frequent push is every 15mins. That is too long an interval to know and act on important matters. Is there anything else I can do? The beauty of this phone would be defeated if I would have to mailbox and wait every time for the mails to load. My old Samsung which is not even top of the line gives me my email faster and I get to act upon work ASAP. When new mails come I see it right away, no more waiting time needed. Would anybody know if Apple fix this already? If not, I hope they do it really soon. This is a big let down for me. The apps are great including usability in terms of networking, images, etc but let's face it, personal and work email is more important than Facebook, YouTube and everything else. A good techie or Apple I hope you can help me or fix this with a system update, ASAP. Thank you very much.