Jesus previously showed how John is a witness that supports Jesus's claims. However, Jesus shows even more support for Jesus's claims.
Jesus's works are an example of testimony (evidence) from the Father (5:36). The Father enables Jesus to do all sorts of miracles in the first place.
The Father himself has testified of Jesus because the Father sent Jesus (5:37). The evidence is written in past Scriptures (5:39), especially in Isaiah that specifically foreshadows the person now known as Jesus. Even the Pentateuch (first five books of the Bible) has some foreshadowing of the person now known as Jesus, as seen in Deuteronomy 18.
Although the Jewish leaders may have studied the Scriptures a lot, they missed the point of various Scriptures (especially the ones in Isaiah) because they foreshadow the person now known as Jesus. Thus, even though they may think they focus on God because of their emphasis on the Mosaic Law rules, they truly don't because the Father announces the Son in past Scriptures.
Finally, Jesus brings up how the Jewish leaders "are not willing to come to Him" (5:40). Even with the Sabbath controversies, Jesus's miracles signal that he may be important and would be worth checking, but the Jewish leaders went straight to wanting to kill Jesus rather than even trying to learn if he is legit. And even with all these witnesses, some of the Jewish leaders still do not want to come to Jesus, not just because they doubt the legitimacy of the evidence, but because they just don't want to.