From an evangelical Christian perspective, the most likely author of John 15:5 and 15:8 is the Apostle John, one of the twelve disciples of Jesus Christ. The Gospel of John is traditionally attributed to him, and it is believed to have been written in the late first century.

### Key Points about Apostle John and His Writings:

1. **Identified as the Author**: The Gospel identifies itself through its unique style and content as being attributed to John, who is often referred to as “the disciple whom Jesus loved.” His closeness to Jesus during His ministry gives weight to his account of the events and teachings of Jesus.

2. **Theological Emphasis**: John’s Gospel emphasizes the divinity of Jesus and includes much about His teachings, miracles, and the nature of His relationship with believers. This theological depth is evident in the verses from Chapter 15, where Jesus speaks of Himself as the “true vine” and His followers as branches.

3. **Verses in Context**:
– **John 15:5**: “I am the vine; you are the branches. Whoever abides in me and I in him, he it is that bears much fruit, for apart from me you can do nothing.”
– **John 15:8**: “By this my Father is glorified, that you bear much fruit and so prove to be my disciples.”

In these verses, John conveys profound theological truths about the necessity of a relationship with Jesus for spiritual vitality and productivity. This metaphor illustrates the intimate connection between Christ and His followers, emphasizing dependence on Him for spiritual growth.

4. **Evangelical Teaching**: Evangelical Christians often highlight these verses in discussions about discipleship, spiritual fruitfulness, and the importance of a personal relationship with Jesus. The metaphor of the vine and branches is used to teach that true spiritual life and effectiveness come from remaining connected to Christ.

5. **Historical Context**: John’s Gospel is considered unique compared to the Synoptic Gospels (Matthew, Mark, and Luke), with a more reflective and theological approach. The context of 15:5 and 15:8 fits well in Jesus’ Farewell Discourse, where He prepares His disciples for His impending departure, emphasizing the vital role of abiding in Him.

In summary, from an evangelical Christian perspective, the Apostle John is seen as the most likely author of John 15:5 and 15:8, with these verses reflecting key themes of dependence upon Christ and the call to be fruitful disciples.