Yes. Five weeks is enough for the skin to regenerate. The collagen production will likely continue even after that but the TCA peels will not interfere with that.
See also this thread:
https://http://forums.owndoc.com/dermarolling-microneedling/Chemical-peels-in-between-facial-dermarolling
Classification of chemical peels: Exfoliation - can be used daily AHA 5-10%
Retinoids
Very superficial peels Alpha-hydroxy acid (AHA) - glycolic acid and lactic acid up to 50%
Beta-hydroxy acid - (BHA) - salicylic acid (excellent for acne prone skin since it cleans pores)
Trichloroacetic acid (TCA) up to 10%
Superficial peels - reach the epidermis - usually performed every 4-6 weeks TCA up to 30%
AHA - up to 70% (left from 2 to 20 min)
BHA
Jessner’s solution – (contains 14% resorcinol, 14% salicylic acid, 14% lactic acid and ethanol)
Medium depth peels - reach the papillary dermis - usually performed once in 6-12 months. TCA 30% to 40%
Glycolic acid 70% + 35% TCA
Jessner’s solution + 35% TCA
Glycolic acid 70%
Deep peels - reach the reticular dermis - Can be performed once every few years or once in a lifetime. TCA 50% or more
Phenol
The depth of penetration depends on many variables: The concentration of the peel
The pH of the peel
Thickness of the skin
How many layers of the peel are applied
How long it stays on