It has always concerned me that those who hold to the doctrines of grace or "Calvinism" as it is sometimes nicknamed get labeled as anti-evangelistic, anti-missions, or even anti-church. William Carey, the "father of modern missions" and founder of the 'Baptist Missionary Society' gave his life to proclaiming the gospel in India and spurred on thousands upon thousands to follow God's call to herald the good news to the nations- "Tell of His glory among the nations, His wonderful deeds among all the peoples" (Psalm 96:3). This same trailblazer was a faithful preacher and teacher of the doctrines of grace because he understood them to be Biblical truths. So to hold to God's sovereignty in all things- particularly in regards to salvation is not un-evangelistic. To be evangelistic is simply to herald the good news... the good news is that God has chosen to show mercy to people incapable of saving themselves and He did so by sending His Son to pay the penalty of sin on our behalf through His death on the cross. It is not a contradiction hold a belief in the sovereignty of God in salvation and a belief in the responsibility of every believer to share the gospel. In fact it is implicit in these five traditional doctrines that the grace which God has poured into His elect must pour from His elect. It pours from the elect so that those still dead in their sins may hear the good news and gloriously respond to God's call. This sixth aspect or doctrine of grace can be coined the Stewardship of the Gospel.
We are responsible for the gospel of God's grace (Ephesians 3:1-3, 8-10; 1 Thessalonians 2:4; 2 Timothy 1:14). To put it another way, if grace is present within us, it will overflow from us (John 13:35; 1 John 3:14). Of course evangelism shouldn't be like door-to-door sales (2 Corinthians 2:17), invitational response times after sermons should not be for manipulating false decisions or to produce numbers for bragging, and church growth should not be about getting a big crowd for pride's sake. We are commanded to share our faith however- invitations (when done properly) encourage a public response to the inner-working of the Holy Spirit in a person's life and churches can get big if it is healthy growth. These are the outpourings of God's grace in your life and in the lives of the community of faith. Recipients of God's grace are explicitly commanded to herald the gospel (Matthew 28:19-20; Psalm 67:3-4; Psalm 68:3; 1 Corinthians 1:17-18).
A rebuttal to this may be (from a hyper-Calvinist), "Yeah but if God has elected some to salvation they will get saved whether we share or not so why share?"
Why? Because this is how God's salvation plan works- He uses those who were once His enemies to be His heralds to those who are presently His enemies that they too may share in His goodness. This is especially glorifying! We don't know who the elect are- only God knows- so we must proclaim the truth and allow the Holy Spirit to call them unto salvation (1 Corinthians 1:23-24; Romans 10:14-15). If I didn't believe this- if I were instead an Armenian I could never pray for the lost, because how could I pray for God to save the lost if I held that God's will doesn't presume upon men's free will? Thankfully my salvation is anchored in God's will and I recognize that I am now a steward of the grace He has given me to pray for the lost world and proclaim it in every way, to everyone, everywhere God calls.