The answer to your question will depend greatly on what you count as "writing".

The oldest proper writing system is Sumerian cuneiform (just edging out hieroglyphics by a century or two). There are written symbols called "proto-writing" which predate this (like the Vinča symbols and the Dispilio Tablet which date to the 5th to 6th millennium BC. However, they do not appear to be a "language" per se. They are symbols which convey some sort of meaning, but they lack the organization and do not represent a language, so they are not classified as writing. According to the University of Nevada, Las Vegas professor JM Stitt,

A true writing system must be able to represent graphically any utterance of which a language is capable; incomplete systems, such as pictograms, are called protowriting

Proto-writing often (but not always) leads to writing. Both cuneiform and hieroglyphs have proto-writing systems that they developed from, but in different ways. The ways the writing was conceived of was similar and yet different at the same time. The development of the cuneiform writing system is very interesting, and is outlined in Denise Schmandt-Besserat's book "From Counting to Cuneiform" Austin: University of Texas Press, 1992.

According to her, it originated in the Neolithic period, when tokens were first used to mark down how many items were being exchanged in a transaction. These tokens would be little models of the item, and they were enclosed in a clay envelope. Of course, that meant to see them you had to break the clay envelope. To prevent the need to break the envelope, the tokens were pressed into it, leaving the impressions. Then people realized you didn't actually need the tokens at all, just the impressions were enough. The impressions became more stylized pictures, such as can be seen in the Kish Tablet from ~3500 BC, and eventually developed into the full-on cuneiform we know today, with full-on cuneiform writing arriving around 3100 BC in the Jemdet Nasr period. So cuneiform writing was derived primarily from economic transactions and the need to record them, and was derived from logographs.

Egyptian writing developed in a slightly different way, according to Arnett, William S. The predynastic origin of Egyptian hieroglyphs: evidence for the development of rudimentary forms of hieroglyphs in Upper Egypt in the fourth millennium BC. University Press of America, 1982.

Arnett suggests that Egyptian hieroglyphs were derived originally from their art. In fact, when you see Egyptian art, sometimes it's possible to actually "read" the art, as many of their hieroglyphs are scaled versions of drawn things, and so Egyptian murals full of fanciful figures are in fact also conveying linguistic meaning (for more on this see Wilkinson, R. H. (1992). Reading Egyptian art: A hieroglyphic guide to Ancient Egyptian painting and sculpture. London: Thames and Hudson). Later on, this developed into a rebus system, where words were constructed of pictures of things whose sounds resembled other words. An example in English might be the way that a picture of a bee next to a picture of a leaf could be "read" to mean "belief".

The exact point at which hieroglyphs made the transition from proto-writing symbols to genuine graphical depictions of language is uncertain. As far as I am aware, the earliest full sentence we have recovered is from the reign of Seth-Peribsen of the Second Dynasty of Egypt (~2800 BC), though we have found the name of Iry-Hor, a predynastic King of Upper Egypt from the 3100s BC.

That's about all I can tell you about the oldest writing systems. If you assume that proto-writing indicated words (not sure I would agree, it was more about ideas and meaning, rather than reproducing spoken language), then we cannot translate them. If, however, you accept the oldest recorded word as something written in Sumerian cuneiform and recovered at Jemdet Nasr, like this piece here, as it records the Sumerian language in a series of economic transactions, then we have an official writing system that dates to about 3100 BC.