If the five-week old is breastfeeding, that makes it simpler.
If s/he is on formula, you will have to take all the sterilisation equipment, and if any of this depends on electricity I hope the place where you'll be staying has the necessary back-up. Otherwise take sterilising fluid and tank. Use the special purified water (Orbis?) to prepare the formula. It is available from supermarkets and colmados, in the baby products section. Normal 'botell?n' drinking water would have to be boiled first. Dominicans also use botell?n or previously boiled tap water to bath small babies (up to 6 months). I didn't know this and my son got giardia, probably from being bathed in normal tap water.
Is it your first time in the DR?