It is enough for us to know that he bare our infirmities, though free from sin and undefiled. Then, as to the ancient and Levitical priests, the Apostle says, that they were subject to human infirmity, and that they made atonement also for their own sins, that they might not only be kind to others when gone astray, but also condole or sympathize with them. This part ought to be so far applied to Christ as to include that exception which he mentioned before, that is, that he bare our infirmities, being yet without sin. At the same time, though ever free from sin, yet that experience of infirmities before described is alone abundantly sufficient to incline him to help us, to make him merciful and ready to pardon, to render him solicitous for us in our miseries. The sum of what is said is, that Christ is a brother to us, not only on account of unity as to flesh and nature, but also by becoming a partaker of our infirmities, so that he is led, and as it were formed, to show forbearance and kindness. (John Calvin, Commentary on Hebrews 5:1-6)
The Lord Jesus Christ, as Mediator, was and is, as it were, street smart. He welcomed sinners to Himself in order to give of Himself to them, to unite them to Himself and thus redeem and transform them into His likeness. He was not a sheltered "pastor's kid" who recoiled at every sin and slight. He suffered the effects of sin without being contaminated by it, and thus was able to be a sympathetic Savior.
This aspect of His ministry is not among those exclusive to His charge as Christ. His undershepherds would do well to be street smart on account of His sheep.