All five are taught in the Bible and work together in the plan of salvation, in like manner.
Without the Bible as our sole authority we would have no idea what salvation is. The RCC doesn't have a clue how to be saved. They think that it is by works, through the RCC, by baptism, through sacraments, all of which are wrong and heretical. Thus sola scriptura is necessary. ECF cannot be our guide, neither Tradition, neither man. It is sola scriptura.
Sola fide is taught through and through both OT and NT.
Therefore being justified by faith we have peace with God.
There is no clearer statement of sola fide than that. You cannot add anything to salvation. It must be by faith alone.
Sola gratia is by grace alone is so because the Bible teaches it to be so. By denying it one denies the Bible. Even the most elementary student of the RCC will admit this is true.
Ephesians 2:8-9
For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: Not of works, lest any man should boast.
Ephesians 2:5 Even when we were dead in sins, hath quickened us together with Christ,
(by grace ye are saved
Romans 11:6 And if by grace, then is it no more of works: otherwise grace is no more grace. But if it be of works, then is it no more grace: otherwise work is no more work.
--Grace and works cannot co-exist together. It is either by grace or by works; it cannot be both. That is the teaching of this verse.
--The teaching of Ephesians 2:8,9 is that we are saved by God's grace alone, through man's faith alone, in Christ alone. This doesn't contradict anything except the heresies of the RCC.
Solus Christus--means through Christ alone. Do you actually contradict this? What else would it be? Would you include Allah? Is salvation also through Allah? by Brahma? And the various other Hindu deities? In not through Christ alone, are you even saved?
What does this verse mean then?
John 14:6 Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father, but by me.
--He is the ONLY way. There is no other.
Soli Deo Gloria--means "glory to God alone." The RCC has trouble with this also because the glory they give is to Mary and other dead "saints." All glory is not directed to God alone. And if it isn't it is heresy. You would think that this would be such a straight forward doctrine of Scripture, but no, the RCC has to mess this one up as well. They give glory to mere mortals. Glory belongs to God alone.
These are doctrines taught in the Bible, none of which contradict each other; just as none of the persons of the trinity contradict each other.