My ex and I legally have joint 50/50 custody on paper, but our child does not actually live 50/50 between the dad and I. It's really more 70/30. I have our child 5 days/wk. Currently I make about 2-3x more than my ex (rough estimate), I pay benefits for our child and do not receive child support. We have been alternating years on our taxes (we started doing this when our incomes were roughly the same), but I am wanting to discuss with him the possibility of me claiming our child every year and wanted to know what others may think regarding this, and if it's a fair proposal to discuss with my child's father?

You should claim the child, especially given that he/she is with you more than half the year, and you benefit more from the deduction.
Since it sounds like you and your ex are on reasonable talking terms, you can work out a list together of what his costs are, and compare ways of doing taxes with tax software.

Your divorce decree should have specified the terms for claiming the child on your taxes. If not, or if you are trying to circumvent the decree, you will have to work it out amicably with him, and you will need your ex to sign an agreement that must be included with your tax return each year to document that you are the parent who is entitled to claim the child. To help sweeten the deal you might agree to share the tax benefits - for example perhaps you offer to gift your ex $1000/year for allowing you to claim the child.

As circumstances change it's only fair to make adjustments to any agreements we have with others. One would hope that discussion can be civil, but have Plan B ready to go in case it's NOT. Having said that, my question is this, is this a divorce decree or court sanctioned agreement? If not then it may well have to be one. If it is then only a court can modify or change it.

All advice given is sound. Work it out with your ex, and be sure the proper paperwork is submitted.

We have no divorce decree as we were never married. The custody agreement was civil and mutually decided upon, recently finalized to be 50/50 (previously i had full physical and legal and he wanted to change it to include him since he had the child 30% of the time) but our actual custody arrangement with the child has not changed and continues to be what it was before where the child is with me 5days/wk. I am hopeful the proposal will go smoothly. My ex already claims another dependent yearly, so really I could stand to benefit the most from it, especially since I provide more for the child.