Rashi’s translation is based on the Aruch who brings down two different translations and is not clear to him which is correct (the second being Segala). Additionally, the Gemara in Pesachim 35a and a Mishnah in Kilaim 1:1 states directly that שבולת שועל is a sub-species of barley, and this is cited by many rishonim. Oats is clearly not a part of the barley family – it is a distinct species of grain, unlike segala, which is a form of barley.
Furthermore, the Mishnah in Kilaim indicates that שבולת שועל and שיפון and barley can all cross-breed, which is simply false for oats (but true for segala). This ability to crossbreed is explicitly codified in Shulchan Aruch YD 297:14
Lastly, if one simply looks at a picture of oats and compares it to the other 4 grain themselves (Wheat, spelt, barley and rye), oats looks nothing like the other 4. It is clearly a wholly different species.
There is actually a lot more to say and much has been written about this, but it is clear that oats is not one of the 5 grains.