Romans 5 :1-11  Paul gives us 3 reasons to exult:
V2  We exult in hope of the glory of God
V3 We exult in our tribulations, because they will produce perseverance, proven character, and hope;
V11 We exult in God through our Lord Jesus Christ;

The word exult means to rejoice, to glory in, to have joy - We rejoice because we now have hope! 
Paul says that we have been justified by faith - which has been reckoned - computed and declared as righteousness; gaining us admission ( an introduction) into this " grace in which we stand".  We stand "at peace with God through our Lord Jesus Christ".   So yes, we can rejoice!

We can rejoice in our tribulations because we know that God will use them to build our character and that gives us more hope.  " .. and hope does not disappoint, because the love of God has been poured out within our hearts through the Holy Spirit who was given to us." ( v5)

We were helpless, ungodly sinners. We had no hope.  But God, " at the right time" sent Christ to die for us.  "But God demonstrates His own love toward us, in that while we were yet sinners, Christ died for us."  And even more than that; " having now been justified by His blood we shall be saved from the wrath of God through Him."  ( v9).  Once enemies, we are now reconciled.  Once condemned, we are now saved.  We rejoice in God through our Lord Jesus Christ!

Verses 12-21 Paul compares the first man - Adam to the New Man - Jesus Christ.

In Adam - sin entered the world; death came because of sin; sin and death spread to all men;(v12)
               - judgement "arose from the one transgression resulting in condemnation"; ( v16)
               -  by this one transgression " death reigned" ( v17)
               - " through one transgression there resulted condemnation to all men" ( v18)
               - Adam's one act of disobedience caused the many( all) to be made sinners ( v19)
The Law came and pointed out sin.  Sin increased. Sin reigned in death. ( v20-21)

In Jesus - the gift of grace, the Grace of God; " abounded to the many" (v15)
             - " the free gift arose from many transgressions resulting in justification" ( v16)
             -  " much more those who receive the abundance of grace and of the gift of righteousness will reign in life through the One, Jesus Christ."  ( v17)
            - " so through one act of righteousness there  resulted justification of life to all men."  ( v18)
            - Jesus' obedience brings " the many to be made righteous" ( v19)
Grace came to "reign through righteousness to eternal life through Jesus Christ our Lord." ( v21)

Father in heaven, we exult in You. We leap for joy because of Your great Grace towards us while we were still sinners, helpless and condemned.  We rejoice in the hope You have given us through Jesus Christ our Lord! Thank You for saving us. Thank You for justifying us, for declaring us righteous, reckoning our faith in Jesus Christ as righteousness.  Thank You Jesus for abounding in grace towards us, freeing us from sin and death, and giving us eternal life in You.  Amen and amen!