Answer
First, we can't presume that anyone is reprobate unless God specially reveals that information. Reprobation is an eternal decree and hidden/secret by nature. Unless something specific happens to reveal that one is reprobate (direct statement by God, or commission of blasphemy of the Holy Spirit), we cannot know God's decree concerning another individual's salvation/reprobation. Thus, we cannot assume that Jesus' audience in John 5 consisted of reprobate individuals.
Second, God has designed all his eternal counsel to bring glory to himself, but he has not designed all of it to bring emotional pleasure to himself. For example, the Bible specifically tells us that some of his eternal decrees are designed to allow him to express his wrath (e.g. Rom. 9:22-23). God is glorified by expressing his wrath, but he is not therefore happy about it--he is angry. Thus, there is no inconsistency between him longing for the salvation of these people on the one hand, and being wrathful toward them on the other. I would suggest that his "unsatisfied longing" (in whatever way that is possible for God) forms part of the basis for his wrath, so that his desire that these people be saved is not only true, but is a necessary part of his later wrath.
Third, Jesus was not only God, but also man. Most of the time we find him in the Bible speaking from the perspective of his humanity rather than of his divinity. He may have wanted to save them in his humanity, but not in his divinity. I know this sounds weird, but let's face it: the whole God-man thing is weird. Consider the similar situation in Matthew 24:36 where Jesus, who is God incarnate, does not know the eternal decree of God. He can only be speaking from the perspective of his humanity at this point, because in his divinity he clearly must know that decree. In the same way, his humanity was probably also unaware of the reprobation or election of the men to whom he spoke in John 5. Thus, he was not lying. Humanly speaking, he really didn't know whether or not they were reprobate, and he really wanted all of them to be saved. From a human perspective, his statement meant the same thing that you or I would have meant by the same words (though his words were no doubt more heartfelt than mine would have been under the circumstances!). You or I may honestly say to someone, "I tell you the gospel so that you may be saved." All that indicates is that we know that the gospel is the means of salvation, and we hope that when they hear it they will come to faith. It doesn't mean that we know they will or won't come to faith.
Answer by Ra McLaughlin
Ra McLaughlin is Vice President of Finance and Administration at Third Millennium Ministries.