Refactored to have a cleaner API, so users can calculate without explicitly newing up the class.

calculator_service.rb

class Calculator

  ORDERED_OPERATIONS = %W(* / + -) # maintainable, add new operations easily

  # no need to new up if you don't want to.
  def self.calculate(input) 
    new.calculate(input)
  end

  # There is a pathological case where unknown operators are entered. 
  # So input validations would be a good idea in a production setting.
  def calculate(input)
    input = input.split(" ") # doesn't mutate the original input, may have tradeoffs in terms of memory for very long inputs

    while input.length > 1 do # imperative, so 71% faster than recursive according to profiler
      ORDERED_OPERATIONS.each do | op | # runs through each operation til it exhausts them in order
        i = input.find_index(op) 
        # N**2 worst case, but each iteration will be N-2 for each found operation, so closer to N*(N/2) avg.
        # Since N = 4 in the ORDERED_OPERATIONS array it's more like constant. 

        if i 
          prev = input[i-1].to_f # seemed more readable not to dry these up. 
          nex =  input[i+1].to_f
          result = operate(prev, op, nex) # now it accepts whatever operations you want, even custom methods
          input = update_input_with_result(input, result, i) # naming is hard 
        end

      end
    end

    input.first
  end

  private

  def operate(prev, op, nex)
    prev.send(op, nex)
  end

  def update_input_with_result(input, result, i)
    input.slice!((i-1)..(i+1)) #extract evaluated items
    input[i-1] = result #insert result into input
    input
  end
end


input = '7 - 2 + 3 / 4 * 5'
expected = (7 - (2 + (3 / (4 * 5.to_f))))
actual = Calculator.calculate(input)
puts actual
puts (expected == actual)