No.
The issue is the focal ratio at 300mm. Whenever you consider an extender (such as a 1.4x or 2x) you not only have to multiple the focal length of the lens by the extender factor... you also have to muliply the focal ratio as well.
E.g. a 300mm f/5.6 with a 1.4x extender would become 300 X 1.4 = 420mm but the focal ratio becomes 5.6 X 1.4 = f/8.
The problem with this is that almost no camera can focus at f/8... it's too constrained for the AF sensors to work properly. A few cameras can handle it (even though it's not ideal) such as the 5D III and 1D X -- but those are high-end bodies. A T5i wont do it.
Usually a 1.4x extender can be used with a lens if the lens' focal ratio is f/4 or below. A 2x extender needs a lens focal ratio of f/2.8 or below. BTW... even if a lens qualifies the extender still might not work. Canon lists the lenses compatible with their 1.4x and 2x extenders and you'd ultimately need to make sure your lens is on the list.
The Canon EF 100-400mm f/4.5-5.6L IS USM is going to approximately provide the range that you'd get from a 70-300mm with a 1.4x extender, but that's few hundred more than your current 70-300mm DO lens.
And then there's the new EF 200-400mm f/4L IS USM Extender 1.4x which has a built-in extender. Every owner/user waxes poetic and praises the virtues of this lens.... everything except for the price tag (NOT an inexpensive lens.)
Tim Campbell
5D III, 5D IV, 60Da
