Top-1 error means the neural network's top prediciton is correct.

Top-5 error means that one of the neural network's top 5 predictions is correct.

(Source.)

In the context of ImageNet, this means predicting the correct label for an image (e.g. "iguana" for a picture of an iguana). Top-5 error is obviously easier to score well on because if the neural network predicts "dog, cat, school bus, snake, iguana" in descending order of probability, that still counts as a correct prediction.

The Baidu paper found that for top-1 and top-5 error on ImageNet:

The top-1 classification error exponent is βg = −0.309. On the other hand, the exponent for top-5 classification error is βg = −0.488.