Originally Answered: Will a 4' 55 gallon tank fit inside of a 6' 130 gallon tank stand?
The 130-gallon stand is probably about 18 inches wide and (as you said) six feet long.
A 55-gallon tank is 48 inches long and about 12-13 inches wide (on the outside).
It may or may not fit in, depending on what obstructions the stand has to sliding it in there.
It would be easier to comment on this with a picture or a detailed description of the stand, but I assume it has either a shelf underneath (if it was designed to hold two tanks in over-and-under fashion), or some space underneath that you access through doors. Either way, you may be able to get the 55 in there. If it's the kind meant for another tank underneath, the 55 will be smaller than the bottom rack, so you may need to fashion a shelf for it to sit on. If it's the open-space kind, the tank can sit on the floor or on something else you choose to place under it.
In either case, if you use it as a sump, you may have an issue with the amount of space between the top of the sump tank and the bottom of the 130-gallon tank. A typical 55 is about 20 or 21 inches high. A typical manufactured aquarium stand is no more than 30 or 31 inches high (some are shorter). 10 inches of space is probably enough for the hoses and whatnot you need to have above the sump, but with some equipment configurations it might get tight.