I think I have found a tactic but I am not sure if it'll work. The battlefield Yarvin IV allows you to resolve 1 die without resource cost. And the yellow die card crime lords special requires 5 resources to resolve the special is that still counted as a resource cost since most others are placed below the die side where applicable so can I use the claim effect to resolve crime lords special for no cost?

No you cannot. When a die has a 'cost' that cost appears on the face of the die as a tiny resource symbol accompanied by a number. Crime Lord's special does not have a cost; instead, the resources you pay are part of its card ability, and therefore not affected by anything that lets you resolve a die without paying its cost.

This is also in the rules reference, on page 27: