If we are to prove everything by the scripture with His help, we can't take Calvin's side just because we agree with mostly everything Calvin has said as being scriptural truth because not everything he said can be backed by scripture.
1. Total Depravity (also known as Total Inability and Original Sin)
2. Unconditional Election
I agree with the first, but the second needs some clarification that can be seen as reproof for what unconditional election should mean.
Man cannot save himself as in agreement with point # 1, but there is a method to God's choosing whom He will save from those that He will not.
God knows whom are seeking Him to be saved by Him from those that prefer their evil deeds rather than come to the Light to be reproved of them.
John 3:18 He that believeth on him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God. 19 And this is the condemnation, that light is come into the world, and men loved darkness rather than light, because their deeds were evil. 20 For every one that doeth evil hateth the light, neither cometh to the light, lest his deeds should be reproved. 21 But he that doeth truth cometh to the light, that his deeds may be made manifest, that they are wrought in God.
So not only is our believing is a work of God Himself, but the Father chooses whom He reveals His Son to and thus enabling us to believe from those that prefer their evil deeds.
Jesus warned about this to His disciples as well as giving them a promise of how God is at work saving people.
Matthew 7:6 Give not that which is holy unto the dogs, neither cast ye your pearls before swine, lest they trample them under their feet, and turn again and rend you. 7 Ask, and it shall be given you; seek, and ye shall find; knock, and it shall be opened unto you: 8 For every one that asketh receiveth; and he that seeketh findeth; and to him that knocketh it shall be opened.
So the Father is a work here in choosing whom He will draw and reveal His Son to.
John 6:44 No man can come to me, except the Father which hath sent me draw him: and I will raise him up at the last day.....65 And he said, Therefore said I unto you, that no man can come unto me, except it were given unto him of my Father.
Matthew 11:25 At that time Jesus answered and said, I thank thee, O Father, Lord of heaven and earth, because thou hast hid these things from the wise and prudent, and hast revealed them unto babes. 26 Even so, Father: for so it seemed good in thy sight. 27 All things are delivered unto me of my Father: and no man knoweth the Son, but the Father; neither knoweth any man the Father, save the Son, and he to whomsoever the Son will reveal him.
We can see proof of how God the Father works in choosing whom to save between whom were seeking Him from those that were not at the time in the Book of Acts.
Acts 16:6 Now when they had gone throughout Phrygia and the region of Galatia, and were forbidden of the Holy Ghost to preach the word in Asia, 7 After they were come to Mysia, they assayed to go into Bithynia: but the Spirit suffered them not. 8 And they passing by Mysia came down to Troas. 9 And a vision appeared to Paul in the night; There stood a man of Macedonia, and prayed him, saying, Come over into Macedonia, and help us. 10 And after he had seen the vision, immediately we endeavoured to go into Macedonia, assuredly gathering that the Lord had called us for to preach the gospel unto them.
So God the Father knew people were seeking Him spiritually in Macedonia at that time whereas they were not seeking Him spiritually at that time in Asia nor Bithynia, even if they were both not consciously seeking Him or consciously not seeking Him, but the Father knew whom would receive His Son from those that prefer their evil deeds.
3. Limited Atonement (also known as Particular Atonement)
I believe the elect are the firstfruits; the disciples that are abiding in Him to be received to the Marriage Supper as vessels unto honor in His House, but those that are His, but did not depart from iniquity by faith in Him as their Good Shepherd in running that race, will be left behind to be received later on as vessels unto dishonor in His House after the great tribulation.
So Limited Atonement being assigned only to the elect is not true since those left behind that are not the elect, still have that atonement as their works of iniquity on that foundation will be burned up, but that foundation as in that atonement remains.
The way Calvin goes about explaining this can be seen as overdone. God the Father reveals His Son to those that seek Him. enabling them to believe, and thus giving them to His Son to keep as saved, regardless of how they build on that foundation; they will be raised in the last day, but every man in his order; Christ the firstfruits and then they that be Christ's at His coming.
John 6:39 And this is the Father's will which hath sent me, that of all which he hath given me I should lose nothing, but should raise it up again at the last day. 40 And this is the will of him that sent me, that every one which seeth the Son, and believeth on him, may have everlasting life: and I will raise him up at the last day.
5. Perseverance of the Saints (also known as Once Saved Always Saved)
Jesus will finish His work even in those saints left behind for not looking to Him as their Good Shepherd for help in discerning & departing from iniquity as their works that deny Him on that foundation will be burned up.
The idea that no matter what you do, you are saved, is overlooking the warning that it is a terrible thing to fall into the hands of a living God. Stripes will be coming, and those living that get left behind, will face the fire coming on the earth that will burn up one third of the earth ( the entire western hemisphere ), serving as a catalyst for the subsequent great tribulation, creating the new world order, and setting up the mark of the beast system to buy & sell after pooling resources in order for the world to survive after that calamity... which the heat will still be unbearable during that time on the rest of the world.