J.K.
5 year old little boys do not like "paperwork". Girls will sit and write, draw and color or hours at that age but boys... its not usual! My son struggled through kindergarten and I was ready to pull my hair out by the end of the year.
Talk to your sons teacher... tell her the struggle you are having, maybe ask if you can get the Thursday homework on Monday so you can work 1 or 2 pages a day instead of more and have him pick one he wants to do (like coloring) and then you pick one he will not like so much. Also let him trace correctly formed letters that way he gets comfortable with the flow of the letter and more comfident in himself. He may never have perfect, neat handwritting but learning to correctly form the letters is important. I'm not sure where the "I can't" thing comes from either but somehow they learn that at school. Always enocourage him when he tries even if he does it wrong. If you can read the letter... let that be good enough for now. He may not get A's in hand writting but his confidence will grow and he will not get so down on himself.
Also, let him have some play time after school before you start doing any homework. Yes it is important to get it done and you don't want them exhausted but you want them to have gotten rid of the built up energy from being in school all day before trying to make them calm down and focus. Same goes on the weekend. Let him play for awhile before you have him do work but not too late he is tired.
I had to take my sons xbox away (at about 2nd grade) during the school week because he rushed through work. We talked about it and decided that grades, church and sports was more important than t.v. and xbox. So now there is no need to hurry through homework because he is not gonna get t.v or game time anyway. But I do allow him to earn it with great effort, good grades and hard work. If he takes his time and completes his homework correctly and neatly the first time... he can earn some tv or game time that night after chores and other activities are done too. He is in 5th grade now and doing fine in school so this worked some for him.
Good luck, been there. Hope it helps:)