If you know nothing of Calvinism or Armenianism and just read the Bible with an open mind and allow the holy Spirit to guide you, Then there is no way you can not see that all 5 points are very scriptural. However, This is VERY difficult to do. Most people already have preconceived notions on this topic and when you go to the Bible trying to find support for preconceived ideas, You can find verses to support almost anything (including contradictory things).
All of the doctrines of grace (TULIP) are found textually throughout the Bible. The biggest ongoing debate over this topic is not whether God is sovereign, but whether God chooses us, or we choose God. Ephesians 1 makes it clear that God chose us before the foundation of the earth to be holy and blameless before Him. If man was required to choose God to be saved, no one would be saved because we simply DO NOT want God in our natural state. The main argument against predestination is free will. "God gave man free will to choose God, and God cannot violate man's free will." Let me ask you a question here. How Big is your God? If man has the right to resist the grace of the Almighty God, how big does that make God? You are literally elevating man above God by saying that man can decide whether or not he wants to be with God for eternity or not. That would be like a piece of clay deciding not to become a piece of pottery. The clay has no right over what the potter wills it to be molded into. The same principle goes with God. God is the Potter and we are His clay. We cannot decide whether we are going to heaven or not. It's entirely up to God. He created the Universe, therefore, He has the right to do whatever He wills to do.
You can find the idea of election being traced back throughout the Old Testament. Not to mention the fact that salvation is explicitly said to be designed in such a way so that no man can boast. Unconditional election is the only way that man has no boasting rights to his salvation. Not to mention that it's highly biblical (1 Corinthians 1:27-29 is the first passage that springs to mind).
The sovereignty of God regarding the salvation of sinners is through out the bible in both the old and new testaments. Paul makes this abundantly clear in not only Romans but in Ephesians, and other parts of the pauline corpus. And not only Paul but Christ does in the gospel of John.
Calvinists use Romans 9 to justify their beliefs, but it is grossly misinterpreted. To further the troubles of Calvinism, it was essentially a childish response to the five points of Arminism at the Synod of Dort, some fifty five years after John Calvin died. Calvin himself had nothing to do with the Five Points of Calvinism
Let me first address the Doctrines in calvinist sorteriology listed through the acronym TULIP which require the plain meaning of the bible to be twisted:
1. U- Unconditional election:This doctrine teaches that people are elected to salvation before they were born or Christ even died on the cross. However, The bible teaches clearly that salvation is received upon putting faith in Jesus (Acts 16:31, Romans 10:9)
It also contradicts the clear Bible teaching that God desires for all people to be saved(1 Tim 2:4)
2) L-Limited atonement: This doctrine is in Total contradiction to the teaching that Jesus Died bearing the sin of the whole world. (1 John 2:2)
3) Irresistable grace: This doctrine contradicts the clear biblical warnings to not harden our hearts against the holy Spirit; claiming that its impossible to resist the Holy Spirit when it comes to salvation.
4) Perseverance of the Saints:
Again this doctrine negates the clear teaching in the bible about true Christians falling away/Being removed from union with Jesus. There is no guarantee that all christians will persevere, but rather some are expected to fall.(John 15:6, Hebrews 4:1 & 11;Rev 3:5;Rev 3:16 etc)