[raybbr]

Light from this explosion traveled through space for 5 billion years before slamming into Swift, overwhelming its X-ray camera. The observatory, launched in November 2004, was designed specifically to hunt for gamma-ray bursts, though scientists didn't count on a blast quite so strong.

How could they possibly know the date of origin?

[HiTech RedNeck]

The standard calculations of old-universe, big-bang cosmology are implied here. It's explained at various old earth creationist sites as www.reasons.org

[al baby]

They base it on the gulf oil rig explosion times the number of days till obama is out of office divided by the number of days it has been leaking then the you take the number of states 57 whichever is bigger

[C19fan]

I would guess like Hubble did with visible red shift there is a similiar doppler effect in the EM spectrum of these bursts.

[Nateman]

How could they possibly know the date of origin?

Here is how.

[hc87]

How could they possibly know the date of origin?

It's 5 billion light years away.

They estimate the distance by using Type Ia supernovas as a benchmark standard. Type Ia supernovas always erupt with the same amount of energy, thus you can measure the luminescence of a type Ia supernova in a distant galaxy and estimate the distance to that galaxy by measuring the ratio of light observed, as compared to Type Ias in our galaxy.

Distance in our galaxy, by contrast can be measured by several other methods, including parallax (looking at a star from different points in the Earth's orbit and then use simple geometry to calculate distance) and looking at light emitted by a variable star type called a Cepheid (same principle as Type Ia supernova measurement). There are also several more exotic means of measuring light from other types of nova that give distance results on a galactic scale.

Long story short, it involves lots of math and physics.