I'll take a crack at this, though I'll be up front and admit that I've never worked with iPhone 5 footage in an editing application.
You're approach to rendering video is for the most part sound. Like you've done, it is best to export with the same codec as your imported footage. However, in this case, the iPhone 5 video preset (either .mp4, .mov, or .m4v) likely has a very low bitrate setting. Thus, selecting "match media settings" in Vegas may be heavily compressing an already compressed video. This can result in a ton of compression artifacts and smudgy video.
Have you tried rendering out to an acceptable higher bit rate codec? I would suggest either ProRes 422 HQ (if you have the Apple ProRes QuickTime component installed) or H.264 with a bit rate of 35 Mbps or above. That may help you to overcome the rendering issues you're having. Also, it's important to keep the frame rate settings, interlace settings (iPhone should be progressive, or no interlacing), aspect ratio, and frame size from the original video. Just a thought!