Jesus said, “Without Me, you can do nothing” (John 15:5b). I assume He meant good things; does that also mean that we use His power also when we sin and do evil?

In the context of this well-known verse, Jesus is drawing a picture of a vine and its branches. He identifies Himself as the vine and the disciples (this conversation is taking place in the Upper Room just prior to Gethsemane and all that is to follow). Here is the entire context: I am the true vine, and my Father is the gardener. He cuts off every branch in me that bears no fruit, while every branch that does bear fruit he prunes so that it will be even more fruitful. You are already clean because of the word I have spoken to you. Remain in me, and I will remain in you. No branch can bear fruit by itself; it must remain in the vine. Neither can you bear fruit unless you remain in me. I am the vine; you are the branches. If a man remains in me and I in him, he will bear much fruit; apart from me you can do nothing. If anyone does not remain in me, he is like a branch that is thrown away and withers; such branches are picked up, thrown into the fire and burned. If you remain in me and my words remain in you, ask whatever you wish, and it will be given you. This is to my Father’s glory, that you bear much fruit, showing yourselves to be my disciples. As the Father has loved me, so have I loved you. Now remain in my love. If you obey my commands, you will remain in my love, just as I have obeyed my Father’s commands and remain in his love. I have told you this so that my joy may be in you and that your joy may be complete—Jesus Christ, John 15:1-11. What Jesus is declaring to the disciples is their purpose in life—to bear fruit, in fact, to bear much fruit—and the only means by which that can be accomplished—remaining in Christ, remaining connected to Him even as a branch, to remain viable, must remain connected to the vine. A branch cut off from the vine cannot hope to bear any fruit; it will be unable to fulfill its purpose. And more than just bearing fruit occurs if we remain connected to Christ: God the Father is glorified. And, in addition to remaining connected to bear fruit, being connected to Christ also keeps planted in His love, in a connection that will remain. That’s where the joy of life is—both for us and for Him.
Now, regarding the capabilities of our various abilities, while the most obvious response to this question would be “yes,” actually this verse is suggesting more. One of the great verses found in Scripture regarding God’s love for all is from the Sermon on the Mount, where Jesus said, He causes his sun to rise on the evil and the good, and sends rain on the righteous and the unrighteous—Jesus Christ, the Sermon on the Mount, Matthew 5:45b. In other words, God blesses all in universal ways, regardless of their relationship with Him. He has given all people—saints and sinners—gifts of His grace in their talents and abilities that allow for great accomplishment in this world. And obviously, many great things have been done by those who had no regard or even conscience for God’s sustaining power. It was all them, in every context. I bring that up only to point out the fundamental construct of Christianity—that it is built on our helplessness. I can know nothing of life without being sustained by God—down to the smallest increment. In fact, that is where the true joy of the life can be found, in realizing just how deeply and completely God allows me to know and experience anything. However, when I am living for myself, pleasing for myself, accomplishing for myself, while I may be doing that with the abilities God gave me, I am NOT in any way doing it in His power. His power only accomplishes God, because it operates in harmony with the will of the Father. Nobody knew that better than the Son; as Jesus said, I tell you the truth, the Son can do nothing by himself; he can do only what he sees his Father doing, because whatever the Father does the Son also does—Jesus Christ, John 5:19. For the Christian, as we continue in the life, the question should quickly become apparent, Why would I even want to try and do anything apart from Jesus? Being with Jesus, becoming like Him—that’s where the blessing is.