The Thirteen Paths give power to the light-loving-kindnesses of malchut , strengthening them over her judgments. This is called in Kabbala “sweetening the judgments”. This saves malchut from the kelipot. If, however, the judgments are sometimes too strong to be sweetened, then these five loving-kindnesses come to the rescue. This can be compared to cinnamon which on its own is bitter (representing judgment). The proper amount of sugar (representing loving-kindness) will sweeten it. If however there is too much cinnamon, the sugar won’t ameliorate it. You would then need to add honey to sweeten it. Therefore the five loving-kindnesses are called sepals because they protect malchut where the thirteen petals aren’t enough.
Now the Zohar’s analogy comes into full focus. The rose protects its vulnerable inner parts with thirteen petals and an outer casing of five stronger petals. In the same way the Thirteen Paths of Mercy and the five chasadim protect the balance of judgment and loving-kindness within malchut. It is this mechanism of balance which protects from the kelipot.
"…and they are five gates":Bina is the eighth sefira from the bottom. Thus it is one step above the natural world, which was created in seven days from the lower seven sefirot. Therefore the sefirot of bina are called “gates” because they are openings to the realm above.
"And concerning this secret it is written, ‘the cup of salvations shall I raise.’":
The “cup of salvations” refers to the ritual cup of blessing which is filled up with wine, and over which benedictions are recited (e.g. for Kiddush, Havdala, etc.).
The allusion here is to the “cup” (i.e. “vessel”) of malchut being raised up (i.e. protected by) the five fingers (chasadim). The cup, which is a vessel, is filled up with wine. Metaphorically malchut is filled up with the “wine” of the sefirot above. It is then raised signifying its being taken out of reach of the kelipot.
The Hebrew word for cup, “kos" has the numerical value of 86. This is the same numerical value as the divine name Elokim, which corresponds to malchut.
As the Zohar is referring here to the cup of blessing filled with wine, it is worth mentioning that the numerical value of the Hebrew word for “wine”, “yayin”, is 70 - exactly the same as the Hebrew word for “secret”, “sod”. “Sod" is the deepest level of understanding Torah and corresponds to the Kabbala. Therefore, one who drinks this vintage wine merits salvation. The entire Zohar is from sod, and therefore learning it saves the soul. Indeed the Zohar teaches in reference to itself: “With this book they will go out of exile.”
"…upon five fingers": The cup of blessing is held in the right hand, the side of loving-kindness. Its five fingers therefore represent the five loving-kindnesses.
"…and not more": This means without help from the left hand, which is the side of judgment.
"And the rose…": As mentioned above, the rose is likened to Knesset Yisrael, which in turn corresponds to malchut . The cup of blessing also corresponds to malchut.