In addition to combinatorial/hypergeometric approach in my comment:
By simulation, the probability of a number higher than 95, out of 23 draws without replacement from among numbers $1,2,3,\dots,94,96,97,98,99,$ is $0.663\pm 0.001.$

    set.seed(2020)
    mx =replicate(10^6, max(sample(c(1:94,96:99), 23)))
    mean(mx > 95)
    [1] 0.663096
    2*sd(mx > 95)/1000
    [1] 0.000945304

Unconditionally, the chances the highest number out of $1,2,3,\dots,99$
exceeds 95 is $0.677\pm0.001$ by simulation.

    set.seed(928)
    mx = replicate(10^6, max(sample(1:99, 24)))
    mean(mx > 95)
    [1] 0.677377       # aprx P(max nr > 95)
    2*sd(mx > 95)/1000
    [1] 0.0009349601   # aprx 95% margin of simulation err