Shall i upgrade Database server from 2005 to 2012 without upgrading SSRS or web Application
Will suggest you to go through this whitepaper SQL Server 2012 Upgrade Technical Guide, to get a proper understanding on what all is needed for the activity.

There are many points which would be need to be think upon, i.e.


  Just upgrading by keeping the compatibility level at a older version is not real upgrade. Evaluate at using some of the new features to increase productivity, performance, maintainability and scalability.


As the upgrade talks happens, get started with tracking if any deprecated features are being used. There are multiple ways to do this – I highly recommend using the “ SQL Server: Deprecated Featurese” Perfmon counter to track it like a background task. As your application runs, this gives you a rough idea of how many deprecated features you might be using inside your application that might have an impact to your upgrade process. There is also a Trace Event for capturing Deprecated features with SQL Server Profiler which you can use but that will be to nail down which code is causing that perfmon spike.

Also before upgrading you should check Upgrade Advisor as a first step. This surely guides you of potential problems upfront and is one of the essential step too for any SQL Server upgrade process.

Also, you need to understand on the OS version. If you're current OS running sql server 2005 is good enough to run SQL server 2012.

Similarly, when you check for apps and SSRS, you need to test their functionality if they are designed to run and function as per the latest SQL server 2012 features. 

So, before coming to conclusion you need to have a thorough testing done on test/dev/staging servers to test the above apps\reports.

Get everything documented and then layout a plan to decided a YES or NO.

Hope this helps.