The question is incomplete
The given dimensions are <5, 10, 3, 12, 5>
now we have 4 matrices
1st matrix size 5X10
2nd matrix size 10X3
3rd matrix 3X12
4th matrix 12X 5
let the matrices be A ,B,C and D since we have to parenthesize the matrix chain following cases are possible
Case 1:
(A*B)*(C*D)
Case 2:
(A*(B*C))*D
case 3:
A*(B*(C*D))
case 4:
A*((B*C)*D)
case 5:
((A*B)*C)*D
we have to evaluate each case find the case with minimum scalar multiplications
Case 1:
first we multiply first and second matrices so total number of scalar multiplications are 5*10*3=150
the resultant matrix size is 5X3 let it be T1
then by multiplying C and D matrices total number of scalar multiplications possible are 3*12*5=180
the resultant matrix size is 3X5 let it be T2
finally by multiplying T1 and T2 the total number of scalar multiplications possible are 5*3*5=75
hence total number of scalar multiplications possible are 150+180+75=405
similarly evaluate all the cases and the case with minimum number of scalar multiplications will be the answer