Is it possible to combine all five chakra elements?
Chakra element combination is supposedly a born trait. A shinobi is born with one chakra element, and can master a few more (secondary elements).
However, in some clans, such as the Senju, they were born with two elements, (both Earth and Water), and they could naturally combine them to form the Wood element.
Since we only thought that two element combinations were possible, and we discovered that three were indeed possible, I see no reason why there isn't a possibility for four or more.

 EDIT! Based on the latest manga chapters, it seems as if at least 4 element combination is possible. Although it's an initial estimate and the Third might be wrong about it.

We do have some examples for ninja mastering all five chakra elements, Kakuzu is a great example. He had all five chakra elements, Water, Earth, Fire, Lightning and Wind, in one body (though he did cheat and used 5 different hearts for it). So it is possible. It is also said that those who awaken the Rinnegan can master all six elements (Including the YinYang element).
About mixing them together, since that hasn't happened yet, we can't be sure.
EDIT!

 Six Paths Sage Chakra, which creates the Gudodama is called Kekkei-Mora and was confirmed to be a combination of all 6 elements: Fire, water, earth, lightning, wind and YinYang.