Question: Pascal Triangle over Time

I can calculate the probability of observing 5 heads after a 10 coin toss as:

n := 10:  p :=0.5 :  x := 5 :

ProbabilityFunction(Binomial(n, p), x);

                                0.2460937500


Now my question is how can I generalize this argument over time and with an Normal(0,1) process.

For example what is the probability that after 10 period the sum (integral) of returns represented

drawings from a Normal(0,1) distribution will be smaller than for example -5  or +5.
 

I can calculate the probability that we will for example observe 5 negative returns after 5 periods
 

with(Statistics):
evalf(eval(CDF(Normal(0, 1), x), x = 0), 5)^5 :

                                0.03125000000
 

but it is not that interesting because it is the most unlikely scenario. The most likely scenario would

be to see some negative and positive returns but with an bias towards either side