I am receiving $5,000 from a Trust Company my grandparents set up for when they pass on. I was told that the Trust Company would tax that $5,000 dollars, is that proper and can anyone cite specific references?

Further, I understand that money will not be taxed by the IRS but will it affect my income tax bracket?

Please, if possible, cite sources so I can independently confirm it in case I need to do so. Thank you.

A trust is a separate tax entity which must file its own tax return (Form 1041), so, yes, it IS proper.

So the money from the trust is already taxed before you get it, so it should not affect your tax bracket.