let the two numbers be x and y.
as per 1st condition;
10x + 5y = 170......(1)
as per 2nd condition;
x-y = 5
or x = y+5 ...........(2)
put the value of 'x' from (2) into (1) and we get,
[10(y+5)] + 5y = 170
10y+50+5y = 170
add like terms and we get;
15y+50 = 170
subtract 50 from both sides and we get;
15y = 120
divide both sides by 15 and we get;
y = 8
put the value of 'y' in (2) and we get;
x = 13
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