Nick Reiner says he hasn't even received $5 for the jail commissary from his family's trust ... as his legal team says he's owed $558,000.

Nick's legal team says he hasn't been able to access the family's trust account -- which is worth $1.6 billion -- for even the most basic necessities ... this according to new filings obtained by PEOPLE.

Nick's legal team wrote in the filing ... "Nick still has not been able to access even $5 from his trust to buy basic subsistence items from the jail commissary."

Despite Nick's siblings Jake and Romy Reiner's not wanting him to access the family's trust ... Nick won't be facing the death penalty ... and it's largely due to his family's wishes.

Sources previously told TMZ ... Los Angeles County District Attorney Nathan Hochman took into account that Jake and Romy don't want to see Nick -- who is charged with murder in the first degree with special circumstances in his parents Rob and Michele's deaths -- executed.

Also factoring into the DA's decision was Rob and Michele's firm stance against the death penalty.