Download iPone 5s GSM Firmware

After downloading the firmware from bellow,Press Shift key (Windows user) or Press Option key (Mac user) and then press Reset/Update button in iTunes.For more Details read this article or this article.
Note: Your browser may change the ipsw file into a zip file.In that case just rename it as .ipsw and then iTunes will accept the file.For more details please read those articles given above.

iPhone 5s GSM Firmware

• firmware version 7.1.2 (11D257) Download 
• firmware version 7.1.1 (11D201) Download
• firmware version 7.1.0 (11D167) Download
• firmware version 7.0.6 (11B651) Download
• firmware version 7.0.5 (11B601) Download
• firmware version 7.0.4 (11B554a) Download
• firmware version 7.0.3 (11B511) Download
• firmware version 7.0.2 (11A501) Download
• firmware version 7.0.1 (11A470a) Download