From fig 4.7 in Eysenck's Structure and Measurement of Intelligence. This is using data in which the IQ was tested *three times* over the interval listed and the results averaged. A single measurement at age 5 would probably do worse than what is listed below. Unfortunately there are only 61 kids in the study.
age range correlation with adult score
42,48,54 months .55
The results do suggest that g is fixed pretty early and the challenge is actually in the measuring of it as opposed to secular changes that occur as the child grows up. That is consistent with the Fagan et al. paper cited above. But it doesn't remove the uncertainty that a parent has over the eventual IQ of their kid when he/she is only 5 years old.
Note added: I asked a psychometrician colleague about these results. He thought the correlations seemed a bit high. He looked up another study of 80 kids that appears in Bias In Mental Testing. They found a .7 correlation between scores at 7 and 17. If the score at 7 is noisy (looks like just a single measurement in this study) then the repeat measurement used above might raise the correlation slightly (e.g., by 10 percent?), so I think these results are not entirely inconsistent with each other. Also note I read the numbers above from a graph in a small figure, so there is some uncertainty in the values I reported.