Is 5 months too early to start giving my child solids?

No. At 5 months, the solids (mashed solids, of course) are neither forbidden nor mandatory.
No. 4-6 months is best time to start complementary foods (solids.).
No. Ideally, infants should be breastfed exclusively through the first 6 months. There is not much evidence for most infants (unless there is a family history of allergies and eczema) to support delaying the introduction of solid foods from 4 months to 6 months, however. Introduction of solids before 4 months of life is discouraged.