Since you're given #a>5b# and #b>2c#, it would be useful to multiply #b>2c# by 5 so that both inequalities contain the term #5b#. If you do these, then you get a new inequality:
#b>2c# becomes #5b>10c# when you multiply it by 5.
You can now join up the two inequalities to give #a>5b>10c#. Through this, you can therefore prove that #a>10c#.