Declared Righteous: Romans 5:1

Δικαιωθέντες οὖν ἐκ πίστεως εἰρήνην ἔχομεν πρὸς τὸν θεὸν διὰ τοῦ κυρίου ἡμῶν Ἰησοῦ Χριστοῦ (Romans 5:1 GNT)

Black, M., Martini, C. M., Metzger, B. M., & Wikgren, A. (1997). The Greek New Testament (Ro 5). Federal Republic of Germany: United Bible Societies.

I posted Romans 5:1 from Greek New Testament so that I could give a brief exegetical commentary on the term "righteous" in that verse.  Let's see how the verse is translated in several English translations:

 Therefore, having been justified by faith, we have peace with God through our Lord Jesus Christ, (Romans 5:1 NKJ)

 Therefore, since we have been justified by faith, we have peace with God through our Lord Jesus Christ. (Romans 5:1 ESV)

 Therefore, since we have been declared righteous by faith, we have peace with God through our Lord Jesus Christ. (Romans 5:1 CSB)

 Therefore, having been justified by faith, we have peace with God through our Lord Jesus Christ, (Romans 5:1 NAU)

The Greek word order or syntax is slightly different from the English word order.  The word οὖν or "oun" is a coordinating inferential conjunction and is usually translated as "therefore" in English.  You'll note that the "therefore" in Greek follows the first word in the sentence, which is the key term I want to focus upon here.

Δικαιωθέντες or "dikaiothentes" is a participle.  Participles in Greek have particular meaning depending on the formation of the word, unlike English were tense and mood are often determined by helping verbs.  The parsing guides are helpful here where the participle is parsed and defined:

Δικαιωθέντες verb participle aorist passive nominative masculine 1st person plural from δικαιόω

[GING] δικαιόω

δικαιόω—1. justify, vindicate, treat as just Mt 11:19; Lk 10:29; 16:15. δ. τὸν θεόν acknowledge God's justice Lk 7:29. God is proved to be right Ro 3:4; also Christ 1 Ti 3:16.—2. pass., with reference to people be acquitted, be pronounced and treated as righteous, in theological language be justified = receive the divine gift of δικαιοσύνη Mt 12:37; Ac 13:39; Ro 2:13; 5:1, 9; Gal 2:16f; Tit 3:7; Jas 2:21, 24f. Act., of God's activity Ro 3:26, 30; Gal 3:8; for these and other passages make upright is possible. Make free or pure act. and pass. Ac 13:38f; Ro 6:7; 1 Cor 6:11. [pg 49]   (Gingrich Lexicon, Bibleworks 9.0).

“Dikaioo” is the verb from which the participle “dikaiothentes” is formed. Notice that the participle is in the aorist mood and the passive voice. There is no aorist in English but the combination of voice and mood indicates a completed action that continues on with permanent results. Also, the passive voice indicates that those who have faith have been passive recipients of the declaration of righteousness. That is, they have been acted upon by another. Our righteousness is a legal declaration of “not guilty” in God's courtroom and the basis of that declaration is the active and passive obedience of Christ, who lived a sinless life for His elect and died in their place to take the penalty of sin. The just claim of God's moral law upon us is that we suffer an eternal punishment forever. But Jesus, the only mediator between God and men, took that penalty for His elect in their place (1 Timothy 2:5; Matthew 1:21; John 10:11, 15). And who declares us righteous? Obviously God does.

 "Who committed no sin, Nor was deceit found in His mouth"; 23 who, when He was reviled, did not revile in return; when He suffered, He did not threaten, but committed Himself to Him who judges righteously; 24 who Himself bore our sins in His own body on the tree, that we, having died to sins, might live for righteousness-- by whose stripes you were healed. 25 For you were like sheep going astray, but have now returned to the Shepherd and Overseer of your souls. (1 Peter 2:22-25 NKJ)