One can readily understand that when someone receives two life sentences as logically being the commission and conviction of two separate offenses to which in each case, the criminal has been convicted and sentenced to life, so that, if for some reason, the convict is able to overturn one of the life sentences, he will still have another life sentence to contend with. So too it is fairly easy to understand that life without parole, means exactly that. Then there is the punishment of life imprisonment plus five years or plus twenty years and on the surface, that sounds absurd, but in fact, it makes sense as seen in the first example, in which the person being convicted for life, has that term imposed upon him, and if for some reason that conviction is overturned or served in such a manner that the man can now successfully appeal for parole and is granted it, he still would have an additional five years to serve for another crime that he has been duly convicted of.
Once understanding that, another question comes to mind, as to why doesn't the justice system simply allow the man to serve the second sentence of five years concurrently with the first, especially if the second sentence is something that is not of such a serious nature as to have necessitated a long and lengthy prison term in the first place? It hardly seems like a just punishment to have a man serve thirty years in prison for the commission of a crime, and then only after those thirty years, have to serve even more time, for some other crime, even though he has been in prison for the last thirty years.
It our justice system is so insistent that a man must have two non-concurrent prison terms than it would make more logical sense that the convict serves the lighter sentence first, before having to serve the later one. Their argument against this, I suspect, would be that the lighter sentence may allow that convict to serve his term in a prison system that would treat him "better" than the lowlife that he really is, since his initial servitude would be based specifically on that specific crime and sentence.
Being that as it may, it is a travesty of justice that a man would not serve his sentence for a crime that he has committed, until thirty or even more years have passed after being convicted of such a crime. If the purpose of having convicts be imprisoned is both for rehabilitation and for a just punishment, having a criminal serving a lesser sentence after having being paroled from his previous life sentence, should be seen as a violation of the Eight Amendment against "cruel and unusual punishments".
The justice system should be allowed to convict a criminal for two or more separate offenses, that have two or more separate sentences, but after that conviction, the order of service of those sentences, should be mandated as the lesser sentence being first, and the sentence with the greatest punishment being last; unless the State decides that they wish to begin and to end with the more severe punishment, in which case the lesser sentence(s) must be served concurrently.