Well, trivil, If we assume that A0(H10) was actually intended as A0*H10.
r(H10,T,P,t)=a0*H10 + a1*t + a2*t^2 + a3*T + a4*P + a5
First, set up a matrix. Assuming you have variables, as COLUMN vectors, for the variables: H10, T, P, t and r.
M = [H10,t,t.*t,T,P,ones(n,1)];
The vector a012345 will contain the coeffiicients you wish to find.
You could also use tools from the stats toolboix, such as regress, etc.