Oops

$\Rightarrow 3^{x}+5^{x}-9^{x}+15^{x}-25^{x}$

$\Rightarrow 3^{x}+5^{x}-3^{2x}+3^{x}\cdot5^{x}-5^{2x}$

$\Rightarrow 3^{x}+5^{x}-(3^{x}-3^{x} \cdot 5^{x}+5^{2x}-3^{x}\cdot5^{x}+3^{x}\cdot5^{x}$

$\Rightarrow 3^{x}+5^{x}-(3^{x}-5^{x})^{2}-3^{x}\cdot5^{x}$

Therefore , when $x=0$ , the value of expression comes $1$ as maximum value.

Answer : $\boxed{0<M<2}$

For positive x the value of 25 increases greater than other which will result info negative. For x=0 the answer is 1. For negative x, because all are fracs it will stay on the near zero zone. so the only answer that satisfy is 0<M<2

let's take the value of whats given in the question as y. taking values for x as positive, we get only negative y. so, we have to take negative values for x so as to get max value of y i.e. M. let x= -k. now we write y in the form of k. taking l.c.m. we get, y={ 5^k+3^k+1- (5/3)^k - (3/5)^k }/ 15^k 5^k+3^k+1 can never be much greater than 15^k if we take k values as positive. the rest terms are being subtracted, plus they wont amount to much comparatively to 5^k+3^k+1. which is why i picked my answer to be 0<M<2. of course, there could have been a better solution. critics are always welcome :)