To simplify the expression, we can rewrite it as:

5/(1.2.3) + 5/(2.3.4) + ... + 5/(99.100.101)

Now, let's find a pattern in the denominator:

1.2.3 = 6
2.3.4 = 24
3.4.5 = 60
4.5.6 = 120

We can see that the denominator is increasing by 18 each time. So, the denominator for the nth term would be (n)(n+1)(n+2).

Now, let's rewrite the expression using this pattern:

5/(1.2.3) + 5/(2.3.4) + ... + 5/(99.100.101)
= 5/(1.2.3) + 5/(2.3.4) + ... + 5/(99.100.101)
= 5/6 + 5/24 + ... + 5/(99.100.101)

Now, let's find the common denominator for all the terms:

Common denominator = 6.24.60.120....(99.100.101)

To find the common denominator, we need to find the least common multiple (LCM) of all the denominators. Since the denominators are consecutive numbers, the LCM would be the product of all the numbers from 6 to 99.100.101.

LCM = 6.24.60.120....(99.100.101)

Now, let's simplify the expression using the common denominator:

5/6 + 5/24 + ... + 5/(99.100.101)
= (5 * LCM)/(6.24.60.120....(99.100.101))

Therefore, the simplified expression is:

(5 * LCM)/(6.24.60.120....(99.100.101))