KJV:

5 Now the upper chambers were shorter: for the galleries were higher than these, than the lower, and than the middlemost of the building.

6 For they were in three stories, but had not pillars as the pillars of the courts: therefore the building was straitened more than the lowest and the middlemost from the ground.

NASB:

5 Now the upper chambers were smaller because the galleries took more space away from them than from the lower and middle ones in the building.

6 For they were in three stories and had no pillars like the pillars of the courts; therefore the upper chambers were set back from the ground upward, more than the lower and middle ones.

‫ה  וְהַלְּשָׁכוֹת הָעֶלְיוֹנֹת, קְצֻרוֹת: כִּי-יוֹכְלוּ אַתִּיקִים מֵהֵנָּה, מֵהַתַּחְתֹּנוֹת וּמֵהַתִּכוֹנוֹת--בִּנְיָן.

‫ו  כִּי מְשֻׁלָּשׁוֹת, הֵנָּה, וְאֵין לָהֶן עַמּוּדִים, כְּעַמּוּדֵי הַחֲצֵרוֹת; עַל-כֵּן נֶאֱצַל, מֵהַתַּחְתּוֹנוֹת וּמֵהַתִּיכֹנוֹת--מֵהָאָרֶץ.

The third floor of buildings for the Kohanim is smaller than the first two floors, because the upper part of the galleries is wider than the space occupied by its pillars. To ensure the necessary level of sanctity of buildings for the Kohanim, these buildings should not be in contact with galleries.