I may have misinterpreted your input. However, it seems that your equations can be solved for your unknowns only if the parameters satisfy a compatibility condition. I found a solution for a choice of numerical values of the parameters:
eqs = {rkd ==
RHOK*gx^(1 - RHOK) hk^(GAMMAA) a1kdk^(mu1 - 1) lk^(1 - RHOK -
GAMMAA),
rki == rho*
gx^(1 - RHOK) hk^(GAMMAA) (1 -
a1) kik^(mu1 - 1) lk^(1 - RHOK - GAMMAA),
w (1 + CHII (R - 1)) ==
GAMMAA*gx^(1 - RHOK) hk^(-RHOK) lh^(1 - RHOK - GAMMAA),
rla == (1 - GAMMAA -
RHOK) gx^(1 - RHOK) hk^(-RHOK) lh^(1 - RHOK - GAMMAA),
gx^(1 - RHOK) hk^(-RHOK) lh^(1 - GAMMAA - RHOK) ==
rkdkdk (hk)^(-1) + rkikik (hk)^(-1) + w (1 + CHII (1 - R)) rla*lh};
compatibilityConditions = Solve[Eliminate[eqs,
{hk, lk, lh, w, rla}], rkd][[1]];
Block[{GAMMAA = 1, RHOK = 2, mu1 = 2, CHII = 1, R = 1, a1 = 0,
kik = 1, rkdkdk = 1, rkikik = 1, rki = 1, gx = 1, a1kdk = 1,
rho = 1},
Reduce[eqs /. compatibilityConditions,
{hk, lk, lh, w, rla}]]