I guess Paul had a problem then because he didn't overcome.
For we know that the law is spiritual, but I am carnal, sold under sin. For what I am doing, I do not understand. For what I will to do, that I do not practice; but what I hate, that I do. (Romans 7:14, 15 NKJV)
"For I know that in me (that is, in my flesh) nothing good dwells; for to will is present with me, but how to perform what is good I do not find" (Romans 7:18 NKJV).
"For the flesh sets its desire against the Spirit, and the Spirit against the flesh; for these are in opposition to one another, so that you may not do the things that you please" (Galatians 5:17).
Paul did overcome, he's just explaining about his struggle with the flesh and the fight he was having at times as he denied himself, turning from sin and overcoming his flesh through Christ by the power of the Spirit daily.
He says this in the next chapter
Romans 8
Therefore, brethren, we are debtors, not to the flesh, to live after the flesh. For if ye live after the flesh, ye shall die: but if ye through the Spirit do mortify the deeds of the body, ye shall live. For as many as are led by the Spirit of God, they are the sons of God.
And Paul finished the race
2 Timothy 4
But watch thou in all things, endure afflictions, do the work of an evangelist, make full proof of thy ministry. For I am now ready to be offered, and the time of my departure is at hand. I have fought a good fight, I have finished my course, I have kept the faith: Henceforth there is laid up for me a crown of righteousness, which the Lord, the righteous judge, shall give me at that day: and not to me only, but unto all them also that love his appearing.
Paul also says this
Romans 12
I beseech you therefore, brethren, by the mercies of God, that ye present your bodies a living sacrifice, holy, acceptable unto God, which is your reasonable service.
And be not conformed to this world: but be ye transformed by the renewing of your mind, that ye may prove what is that good, and acceptable, and perfect, will of God
Paul wouldn't have been so strong in the Spirit, and have the understanding that he had, if he hadn't fought his flesh and been overcoming sin in his life, and he couldn't have done it without God. And he wouldn't have preached to others telling them what they are to do before God, if he wasn't doing it himself.
And Galatians 5:17 is about overcoming, meaning you cannot do the things that you please, in other words the Spirit helps us to overcome the things we would do in the flesh and we cannot do them.