According to one site I read, the iP5 supports the mp4 format, which is what my GS4 records. Would there be any reason to convert?
"In terms of TV and Video playback, the iPhone 5 supports
AirPlay Mirroring to Apple TV support at 720p;
AirPlay video streaming to Apple TV (3rd generation) at up to 1080p and Apple TV (2nd generation) at up to 720p;
H.264 video up to 1080p, 30 frames per second, High Profile level 4.1 with AAC-LC audio up to 160 Kbps, 48kHz, stereo audio in .m4v, .mp4, and .mov file formats;
MPEG-4 video up to 2.5 Mbps, 640 by 480 pixels, 30 frames per second, Simple Profile with AAC-LC audio up to 160 Kbps per channel, 48kHz, stereo audio in .m4v, .mp4, and .mov file formats;
Motion JPEG (M-JPEG) up to 35 Mbps, 1280 by 720 pixels, 30 frames per second, audio in ulaw, PCM stereo audio in .avi file format"