I tried to solve the ODE system. But I have a initial conditions are variables. So I want to solve this problem using shooting technique and find the initial values...

(*Define constants*)
phi = 0.5; (*example value,replace with actual values*)
rhoF = 1.0; (*example value*)
rhoS = 1.5; (*example value*)
alpha = 30 Degree; (*example value*)
M = 0.1; (*example value*)
kNF = 1.0; (*example value*)
kF = 0.5; (*example value*)
Pr = 0.7; (*example value*)
CpF = 1.0; (*example value*)
CpS = 1.2; (*example value*)

(*Define the equations*)
eq1 = D[f[eta], {eta, 
       3}]/((1 - phi)^2.5*((1 - phi)*rhoF + phi*rhoS)) + (1/2)*
     D[f[eta], {eta, 2}]*f[eta]*Sin[alpha] + (1/2)*
     D[f[eta], {eta, 2}]*eta*Cos[alpha] - 
    M*(D[f[eta], eta] - 1)/((1 - phi)*rhoF + phi*rhoS) == 0;

eq2 = kNF*D[theta[eta], {eta, 2}]/kF + (1/2)*
     Pr*((1 - phi)*rhoF*CpF + phi*rhoS*CpS)*(f[eta]*Sin[alpha] + 
       eta*Cos[alpha])*D[theta[eta], eta] == 0;

(*Convert to first-order system*)
sys = {x1'[eta] == x2[eta], x2'[eta] == x3[eta], 
   x3'[eta] == -((1 - phi)^2.5*((1 - phi)*rhoF + 
         phi*rhoS)*(1/2*
          x3[eta]*(x1[eta]*Sin[alpha] + eta*Cos[alpha]) - 
         M*(x2[eta] - 1))), x4'[eta] == x5[eta], 
   x5'[eta] == -(kF*
       Pr*((1 - phi)*rhoF*CpF + 
         phi*rhoS*CpS)*(1/2*(x1[eta]*Sin[alpha] + eta*Cos[alpha])*
         x5[eta]/kNF))};

(*Initial conditions for the first-order system*)
ics = {x1[0] == 0, x2[0] == 0, 
   x3[0] == a,(*a should be defined with an appropriate value*)
   x4[0] == 1, 
   x5[0] == b  (*b should be defined with an appropriate value*)};