Q: how do I update browser to safari 7 have 10.7.5

Only by upgrading OS X. You can upgrade to Mountain Lion or Yosemite if your hardware is compatible:

Upgrading to Mountain Lion

To upgrade to Mountain Lion you must have Snow Leopard 10.6.8 or Lion installed. Purchase a redemption code at the Online Apple Store: OS X Mountain Lion. Mountain Lion is $19.99 plus tax. Use the code to redeem a download of Mountain Lion from the App Store. The file is quite large, over 4 GBs, so allow some time to download. It would be preferable to use Ethernet because it is nearly four times faster than wireless.

     OS X Mountain Lion - System Requirements

       Macs that can be upgraded to OS X Mountain Lion

         1. iMac (Mid 2007 or newer) - Model Identifier 7,1 or later.

         2. MacBook (Late 2008 Aluminum, or Early 2009 or newer) - Model

             Identifier 5,1 or later.

         3. MacBook Pro (Mid/Late 2007 or newer) - Model Identifier 3,1 or later.

         4. MacBook Air (Late 2008 or newer) - Model Identifier 2,1 or later.

         5. Mac mini (Early 2009 or newer) - Model Identifier 3,1 or later.

         6. Mac Pro (Early 2008 or newer) - Model Identifier 3,1 or later.

         7. Xserve (Early 2009) - Model Identifier 3,1 or later.

To find the model identifier open System Profiler in the Utilities folder. It's displayed in the panel on the right.

     Are my applications compatible?

         See App Compatibility Table - RoaringApps.

Upgrading to Yosemite

You can upgrade to Yosemite from Lion or directly from Snow Leopard. Yosemite can be downloaded from the Mac App Store for FREE.

Upgrading to Yosemite

To upgrade to Yosemite you must have Snow Leopard 10.6.8 or Lion installed. Download Yosemite from the App Store. Sign in using your Apple ID. Yosemite is free. The file is quite large, over 5 GBs, so allow some time to download. It would be preferable to use Ethernet because it is nearly four times faster than wireless.

    OS X Mavericks/Yosemite- System Requirements

      Macs that can be upgraded to OS X Yosemite

         1. iMac (Mid 2007 or newer) - Model Identifier 7,1 or later

         2. MacBook (Late 2008 Aluminum, or Early 2009 or newer) - Model Identifier 5,1 or later

         3. MacBook Pro (Mid/Late 2007 or newer) - Model Identifier 3,1 or later

         4. MacBook Air (Late 2008 or newer) - Model Identifier 2,1 or later

         5. Mac mini (Early 2009 or newer) - Model Identifier 3,1 or later

         6. Mac Pro (Early 2008 or newer) - Model Identifier 3,1 or later

         7. Xserve (Early 2009) - Model Identifier 3,1 or later

To find the model identifier open System Profiler in the Utilities folder. It's displayed in the panel on the right.

     Are my applications compatible?

         See App Compatibility Table - RoaringApps.

It isn’t possible to upgrade to Safari 7 exactly unless you’re able to get Mavericks from the Mac App Store and have a compatible Mac.

Upgrading to Safari 8 requires upgrading the computer’s OS to Yosemite.

If desired or your Mac’s incompatible with the newer OS versions, you can switch to a product such as Firefox instead.

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If you want to solve your problem you will need new hardware.

Do as Niel suggested: try using Firefox 40.0.3 instead. It is compatible with 10.6.x and higher.