Lord's Day 5 is the first chapter in the Deliverance section of the Catechism. Therefore it is asking basic questions in order to set the stage for future discussion --
Q.12 - how and can we escape punishment?
Q.13 - can we, ourselves, do anything to escape?
Q.14 - can we finagle escape through any other created being?
Q.15 - what sort of mediator is able to do it?
The progression of the questions lays out the direction of the argument - there is escape, but then negative answers to 13 and 14. Finally, 15 establishes what type of mediator is needed. The discussion, of course, is a little more indepth on each of these points. As we have come to expect, Ursinus is exceedingly thorough, and as a result we find that he frequently, even 500 years ago, has asked (and answered) the very questions that continue to confront us in the 21st century.
Q.12 establishes that God's justice, requiring temporal and eternal punishment, must be fully satisfied. There is anticipation that there can be relief based on the promise of Genesis 3:15, but no clear indication how it will be brought about. The prophets of the Old Testament (OT) were deeply interested in how this promise would be worked out. Reading their prophetic statements with 20/20 hindsight we can almost draw a straight line between all of the points, but OT believers lacked our vantage point - like today, they had to take the hidden things of God's promises on faith.
Q.13 states that "we daily increase our guilt" which pretty much puts the kibosh on thinking that we can get ourselves out of this mess. Sort of like a person with credit card debt that is so oppressive that there is no way that they can ever get free because their income cannot even cover the interest. We start out in a hole and every day it gets deeper.
That being the case, Q.14 asks whether there is any other creature we can call on for help? First of all, God will not impose upon any other member of his creation the debt that humans have incurred. OT sacrifices were a picture of the seriousness of the process, with the person offering the sacrifice intimately involved (Leviticus 1:4-6), but the OT sacrifices were not a propitiation for sin. Ursinus also notes that no finite creature can sustain infinite punishment:
A mere creature would be consumed and reduced to nothing, before satisfaction could be made to God in this way: “For God is a consuming fire.” (Deut.4:24)
He also defines a sufficient sacrifice as being measured both by quality (i.e., dignity) as well as quantity (magnitude and duration), and introduces the idea that a sufficient sacrifice must also have a renewing and sanctifying aspect.
Finally, in Q.15, having ruled out that satisfaction can be made on our own, and that we cannot substitute another creature, we come to the conclusion that what is needed is a pure and sinless human who can bear infinite punishment - a human with the strength and holiness of God.
Discussion Notes: Lord's Day 5 repeatedly focuses on the type of satisfaction that is needed to justify humans before God to the extent that one begins to wonder both about his persistence and his audience. In fact this might be one those sections of subtle polemics discussed in the Intro to this class. This led to some exploration of theories of atonement. While these can be clearly delineated on paper, in practice they may be more fluid (some theories may better nuance other theories). Reformed thinking lands squarely on Penal Substitutionary Atonement - penal referring to legal-like action. One is declared guilty or not guilty as a discrete act. One explanation of a Roman Catholic view argued that it would be inconceivable that God would punish an innocent person; therefore Christ's act, instead of punishment, is one of loving obedience earning merit with God the Father. This merit - saving grace - is then accessed through the ministrations of the church. A crucifix, therefore, for the Catholic is a symbol of Christ's love, whereas the Reformed view is more likely to focus on the punishment aspect of the cross. A major difference in application between the two views, is that the judicial view is once for all - It is finished! The believer is justified and adopted into God's family (and then spend the rest of their life learning to live as a child of God). The Catholic view as described in the article, never establishes complete atonement - instead, the grace that Christ merits is accessed through participation in the Church and its sacraments - justification is more-or-less based on a person's sanctification. This may not be a complete or definitive view, since in this podcast a Roman Catholic believer describes his understanding of atonement in agreement with the penal substitutionary view.