There are some good discussions on why one should or should not use the strict mode when coding in JS. I am not going to elaborate on that but rather focus on what to do to write an ExtJs class / app in strict mode.
Before going further, a bit of reading on the strict mode:
ExtJs implements its own class system and basically does not support strict mode (here, here). This is the case with ExtJs 5 too so far. But luckily it will not stop us from creating an ExtJs class with strict mode enabled.
So let's have a look at an ExtJs class with strict mode enabled class wide:
//Make sure strict mode is on
//do some work
this.daNumber = 666;
So far so good, the class behaves as expected, so let's extend it: