The models for both Verizon and Sprint won't let you do other tasks while making a phone call on 4G LTE networks. When you're making a voice call on either of the two networks, you'll need to be on Wi-Fi if you want to pull data inside apps, including the Safari Web browser.
"The iPhone 5 was designed to allow customers to place a voice call on the Verizon Wireless network, while simultaneously allowing customers access to the Internet over the Wi-Fi," Verizon said
"The simultaneous voice and data capability on LTE does not apply to the iPhone," Sprint said.
"AT&T customers have the ability to talk and surf simultaneously on the iPhone 5."