有一个圆形报时机器【钟$$K$$】，特性如下:  与一般时钟相同﹐分针每$$60$$分钟走一圈．不过，时针每$$1440$$分钟走一圈．钟面顺时针方向等距分布【$$1$$】至【$$24$$】(正上方是【$$24$$】)．在【$$5$$时$$x$$分】时，钟面上的【$$10$$】位于钟$$K$$的时针和分针的正中间，求$$x$$的值．  Below is the descriptions of a circular time-reporting machines, namely clock $$K$$.  Similar to normal clock, it takes only $$60$$ minutes for the minute-hand to complete one cycle, but it takes $$1440$$ minutes for the hour-hand to complete one cycle. Numbers to $$24$$ are placed equidistantly on its edge clockwise. ("$$24$$"is at the top of the clock.) At "$$x$$ minutes past $$5$$", the number "$$10$$"lies at the right middle of the two hands of CLOCK $$K$$, find the value of $$x$$. 
选项为:A:$$24$$  B:$$30$$  C:$$36$$  D:$$42$$  E:$$48$$  请回答其中一个选项.