In the probability of 0, 0, 0, 1, 0
What exactly does this thing mean? Is it 00010 or if we assign \mathbf{H}=1 and \mathbf{T}=0, then it is \mathbf{TTTHT}?
Or we can say what is the probability of getting 00010 as 5 digit
Yes, this is like flipping a coin, but with a probability of “heads” being \theta. So the probability of tails is (1 - \theta) on any flip. Each flip is an independent event (which is a well defined term of art in probability theory). If you have independent events, then the probability of a sequence of such events is the product of the individual probabilities. That is how they computed \theta(1 - \theta)^4 in that particular example.
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Exactly and this is joint probability so my guess is correct here