I was dismissed from my job after about 5 months. I did receive one write up while I was working there. Now since my ROE says "MOO" on it, which is the code for dismissed I cannot apply for EI..
Is this dismissal just?

It is very difficult to be terminated for 'cause' (i.e. dismissed), even after only 5 months of employment. You can contest the decision with Service Canada. Also feel free to give us a call at the number below to discuss your situation in more detail. You may still be entitled to a decent severance package, despite your short service.