Hello Shivamsaxena0051,
Thank you for the details of the issue you are experiencing with the battery life and temperature of your iPhone 5. Quitting the applications on your iPhone is a good first step to troubleshoot both of these issues.
The link below has additional suggestions to extend your battery life and also provides information about battery replacement if necessary:
Battery & power
Is your iPhone battery draining too quickly or not holding a charge? Try restarting it first. You can also adjust several settings to extend the battery life of your iPhone.
Find more information here:
iPhone Repair - Battery & Power
http://www.apple.com/support/iphone/repair/battery-power/
Additionally, depending on the warmth of the iPhone, the temperature you are experiencing may be normal. The article listed below explains warmth while charging and using other functions more in-depth:
When using the device or charging the battery, it is normal for it to get warm. The exterior of the device functions as a cooling surface that transfers heat from inside the device to the cooler air outside.
You can find the full article here:
iOS devices: Keeping device within acceptable operating temperatures
http://support.apple.com/kb/HT2101
Your iPhone will warn you if it is over heating, and if it needs to, it will shut itself down. As long as you have not experienced this warning, what you are sensing may be normal. If you believe the temperature is a concern, you can isolate the issue by restoring your iPhone as new. This will help you identify whether it is a hardware or software issue:
Use iTunes to restore your iOS device to factory settings
http://support.apple.com/kb/HT1414
Thank you for using Apple Support Communities.
Best,
Sheila M.