Given how advanced they are, I bet they can exceed 0.5c. They intentionally might not exceed that to avoid time dilation. But, it seems like given their technology, they should be able to do so if they wanted.Time dilation does exist in the Trekverse, given the concept was shown on a classroom board in DS9 when Keiko was teaching children on the station.
I'm pretty sure though that in practice, Starfleet vessels cannot approach the speed of light, only exceed it. IIRC the maximum speed ever listed for impulse was 0.5 c, which would have minimal time dilation. Warp drives travel faster than light, but through subspace, where time dilation isn't really a concern.
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