Would I get LTE from a Verizon iPhone 5 on Rogers?
According to Apple's LTE page I won't be getting LTE?
No, the LTE bands used by Rogers are different than those supported by the Verizon iPhone 5. You will be able to get 3G and voice access, but not LTE.
Yes, that's correct, Verizon's iPhone 5 won't work on the Rogers LTE network.
According to Rogers' iPhone 5 page, the specs include:
In the Apple iPhone 5 page you've quoted, you need to get model A1428 which supports LTE Band 17 (700 MHz). Rogers is explicitly listed there as one of the supported LTE networks. If you want to get an unlocked Verizon iPhone 5 (model A1429 CDMA), you won't be able to use LTE on the Rogers network. You'd be better off getting the unlocked AT&T version.