Sorry, but neither the 4X4 of the 5X5 are under 5'
Each compartment is about 13” and the sides are around 2.
My 5x5 is a little over 6' assembled, and the top and bottom go the full width.
packed it will be some inches longer that 6' the 4x4 will still be over 5" packed,
They are indeed heavy.
A caution on assembling: be sure the middle shelves go horizontally, not vertically. they are the strongest horizontally. if you go with the long boards vertically, and use the support dividers as shelves all the weight will be supported by 4 pins, and you risk the shelf breaking out through the pins with the heavy weight of records. I try to be sure my partial shelves are the end shelves. the bottom most shelf and the middle intermediate shelves will take about anything since the load is purely compression.
And again, for those having a hard time getting one; do a search on C-list for Expedit. There should be a lot available since they are so popular…