Jagl - 20 bytes

Input is in stdin in format (3 4 5 6), output is left on stack:

T~dqZ*S1 5r]%{U*}/b+

Waiting for a response from the original poster about the output format. Since input is specified as "whatever you like", I am going to assume that my input can be an array on the top of the stack. Now takes input on stdin.

Explanation:

T~                            Get input from stdin and evaluate
  dqZ*                      Duplicate, get minimum, and multiply that by 10
      S1 5r]                Swap (so array is on top), push range 1-5 exclusive, and rotate
            %{U*}/          Zip arrays together, and multiply each pair
                  b+P       Get the sum of that, add the common minimum, and print

Jagl Alpha 1.2 - 20 bytes

Input is in stdin in format (3 4 5 6), output is left on stack:

T~dqZ*S1 5r]%{U*}/b+

Waiting for a response from the original poster about the output format. Since input is specified as "whatever you like", I am going to assume that my input can be an array on the top of the stack. Now takes input on stdin.

Explanation:

T~                            Get input from stdin and evaluate
  dqZ*                      Duplicate, get minimum, and multiply that by 10
      S1 5r]                Swap (so array is on top), push range 1-5 exclusive, and rotate
            %{U*}/          Zip arrays together, and multiply each pair
                  b+P       Get the sum of that, add the common minimum, and print

Jagl - 18 or 19 bytes

18 bytes (input is on top of stack, and output is all that is left on stack):

dqZ*S1 5r]%{U*}/b+

19 bytes, (input is on top of stack, output is printed):

dqZ*S1 5r]%{U*}/b+P

Waiting for a response from the original poster about the output format. Since input is specified as "whatever you like", I am going to assume that my input can be an array on the top of the stack.

Explanation:

dqZ*                      Duplicate, get minimum, and multiply that by 10
    S1 5r]                Swap (so array is on top), push range 1-5 exclusive, and rotate
          %{U*}/          Zip arrays together, and multiply each pair
                b+P       Get the sum of that, add the common minimum, and print

Jagl - 20 bytes

Input is in stdin in format (3 4 5 6), output is left on stack:

T~dqZ*S1 5r]%{U*}/b+

Waiting for a response from the original poster about the output format. Since input is specified as "whatever you like", I am going to assume that my input can be an array on the top of the stack. Now takes input on stdin.

Explanation:

T~                            Get input from stdin and evaluate
  dqZ*                      Duplicate, get minimum, and multiply that by 10
      S1 5r]                Swap (so array is on top), push range 1-5 exclusive, and rotate
            %{U*}/          Zip arrays together, and multiply each pair
                  b+P       Get the sum of that, add the common minimum, and print

Jagl - 18 to 21 bytes

18 bytes (input is on top of stack, and output is all that is left on stack):

dqZ*S1 5r]%{U*}/b+

19 bytes, (input is on top of stack, output is printed), just append P

20 bytes, (input is on stdin in the format (3 4 5 6), output is left on stack), just prepend T~

21 bytes, input on stdin and printed output:

T~dqZ*S1 5r]%{U*}/b+P

Not sure what qualifies and what doesn't. Could probably shave a few bytes off, which I will work at.

Explanation:

T~                          Get input on stdin and evaluate
  dqZ*                      Duplicate, get minimum, and multiply that by 10
      S1 5r]                Swap (so array is on top), push range 1-5 exclusive, and rotate
            %{U*}/          Zip arrays together, and multiply each pair
                  b+P       Get the sum of that, add the common minimum, and print

Jagl - 18 or 19 bytes

18 bytes (input is on top of stack, and output is all that is left on stack):

dqZ*S1 5r]%{U*}/b+

19 bytes, (input is on top of stack, output is printed):

dqZ*S1 5r]%{U*}/b+P

Waiting for a response from the original poster about the output format. Since input is specified as "whatever you like", I am going to assume that my input can be an array on the top of the stack.

Explanation:

dqZ*                      Duplicate, get minimum, and multiply that by 10
    S1 5r]                Swap (so array is on top), push range 1-5 exclusive, and rotate
          %{U*}/          Zip arrays together, and multiply each pair
                b+P       Get the sum of that, add the common minimum, and print