If you take a look at these comparisons, through the screen mode, you may be able to get your screen closer to the iPhone 5 BUT one thing that will probably not change is the contrast and brightness (white & black levels).
Checking on the RGB color level comparisons on their CalMan readings, the Note II has much higher greens (edit) and less reds... Blues (edit) may stay the same-ish. The contrast ratio for any Samsung device will always be redonkulous due to the way the screen works... adjusting the greyscale may help (bring it down... labled DE Amp and maybe the max threshold might help with certain things you see on your device... I don't claim to know exactly where to go on your device, just kind of pointing you towards the math that was put out on the color differences between the devices you are curious about so you can make a better guess on where to adjust your screen towards).
Remember: Screen Mode 'Movie' does not move anything on the screen adjustments. Standard or Natural will give you a 'closer to iphone contrast ratio'... otherwise, your Dynamic mode will blow it out of the water. From there, adjust.