Every person, firm, or corporation doing business within this state employing five (5) or more persons, or employing any child under sixteen (16) years of age, shall be subject to the provisions of § 28-3-1 — § 28-3-20 whatever the business conducted by the person, firm, or corporation; provided, that the provisions of § 28-3-1 — § 28-3-20 do not apply to children employed in household service or in agricultural pursuits; and provided, further, that the provisions do not apply to the employment of children in the vocation, occupation, or service of rope or wire walking, or as gymnasts, wrestlers, contortionists, equestrian performers, or acrobats, riders upon bicycles, or mechanical contrivances, or in any dancing, theatrical, or musical exhibition, but the employment of children in any vocation, occupation, or service enumerated in this proviso shall continue to be governed by the provisions of § 11-9-1 — § 11-9-8.