Solution

The $$(C-Br)$$ bond in the case of $$7-$$ bromo $$1,3,5-$$cycloheptatriene is broken easily because the intermediate carbocation formed is very stable (aromatic as it contains $$(4n+2)\pi e^-$$, i.e., follows Huckel's rule), while it does not break easily in the case of $$5-$$bromo $$1,3-$$cyclopentadiene because carbocation formed here is highly unstable as it is anti aromatic i.e., does not follows. Huckel's rule.