It is reasonable, but I'm having trouble finding unambiguous precedent for it in natural languages.
This handout shows the frequency of different orders of demonstratives, adjectives, nouns, and numerals in a sample of 528 languages. Demonstratives and determiners are not identical, but there is considerable overlap.
Num-Dem-N-Adj is not attested.
More broadly speaking, demonstratives seem to show a clear tendency to be closer to the edge of the noun phrase.
From the handout,
The adjective and numeral tend to occur closer to the noun than the
demonstrative when the demonstrative and the adjective or numeral (or
both) occur on the same side of the noun.
Furthermore, in cases where the demonstrative is to the left of the noun, there seems to be a very strong tendency for it to be the leftmost thing.
That being said, a demonstrative is a very heavyweight thing and not always a determiner. Without knowing what kinds of things are determiners in your language, it is hard to tell how much, if at all, the handout applies.
Here are approaches you might want to consider.
Put demonstratives at the right edge of the noun phrase and other determiners directly before the noun.
Demonstratives show a strong but not overwhelming tendency to appear on the opposite side of the noun as the adposition. I think that, in general, demonstratives are not the heads of the noun phrases they appear in cross-linguistically. Since you mention that your language is head-initial, I am assuming that it is prepositional.
Let's assume for the sake of argument that your inventory of determiner prefixes marks definiteness and number only.
The red books
DEF.PLUR-book red that
Those red books
5 DEF.PLUR-book red that
Those five red books
Repeat the determiner on the number
As far as I know, this is also unattested, but it does solve the problem of the determiner not appearing early enough in the noun/determiner phrase.
These five books
Any five books
Make numbers occupy the determiner slot
This works well if your set of determiners is small, but doesn't work very well if it contains demonstratives.
Some 5 books / the 5 books / 5 books
Make the determiner a clitic that attaches to first word in the noun phrase
This doesn't work if your language is fusional and it doesn't make sense to split the prefix from the base noun.