Here’s a helpful quote from NT scholar Douglas Moo on Romans 10:5-13
““Central to the Reformers’ teaching about salvation was their distinction between “law” and “gospel.” “Law is whatever God commands us to do; “gospel” is what God in his grace gives to us. The Reformers uniformly insisted that human depravity made it impossible for a person to be saved by doing what God commands; only by humbly accepting, in faith, the “good news” of God’s work on our behalf could a person be saved. This theological “law”/”gospel” antithesis is at the heart of this paragraph, as Paul contrasts the righteousness that is based on “doing” the law (v. 5) with the righteousness that is based on faith (vv 6-13). Significantly, Paul finds this distinction in the OT itself, manifesting his concern to prove that the gospel that has proved a stumbling block for so many Jews and a foundation stone for so many Gentiles is in continuity with the OT.” (Romans Commentary p 644)”
