Question: Finding coordinate vectors with respect to ordered bases

If S= { <0,1>,<1,2>} and T={<1,1>,<2,3>} are ordered bases for R² and v=<1,5> and w=<5,4>, then can someone help me:

-find the coordinate vector of v and w with respect to the basis T by creating a procedure?

-I can make a procedure to find the transition matrix P_S<-T from T to S-basis, but can you help find the coordinate vector of v and w with respect to the basis S. Using P_S<-T?

Thanks you to anyone who takes the time to help :)