The bacterial transposon Tn10 has previously been shown to move to other genomic sites by a conservative mechanism, whereby the transposon is excised by double-strand breaks and inserted between a pair of staggered nicks at the target. Other transposons, like Tn3, have been shown to transpose by a replicative mechanism that involves symmetrical nicking of the element and formation of the `Shapiro intermediate', which can mature into either a cointegrate or a simple insert. The situation with respect to Tn5 is unclear; it was originally reported to use a conservative mechanism, but other evidence suggests that the mechanism might be replicative. In this paper, rearrangements of adjacent DNA promoted by Tn10 and Tn5 have been compared using positive selection for galactose-resistance to detect such rearrangements. Tn10 promoted the formation of adjacent deletions (that started from an inside end of Tn10), deletion/inversions and simple IS10 insertions, but no cointegrates. This behaviour is fully consistent with a conservative mechanism. In contrast, Tn5 was found to promote formation of adjacent deletions (that started mainly from an outside end of Tn5), IS50 insertions (that were frequently accompanied by inversions of adjacent DNA) and cointegrates. These characteristics seem compatible with a replicative, rather than a conservative, mode of transposition. Clearly, Tn5 and Tn10 exhibit some significant differences in their transposition. These results, and results of some previous experiments, have been interpreted to mean that Tn5 could use a replicative mechanism for its transposition.