Rank each judge's scores separately (highest score = rank 1), then apply Spearman's formula to the two rank columns.

Judge A ranks: 1,3,4,2,5. Judge B ranks: 2,3,4,1,5. $\sum d^2=2$, $n=5$.

$r_s = 1-\dfrac{6\times2}{5\times24}=1-\dfrac{12}{120}=0.9$.

Step 1 — Rank Judge A's scores (highest = rank 1). Scores $45,38,30,42,25$, sorted: $45>42>38>30>25$. Contestant 1 (45)→rank 1; contestant 4 (42)→rank 2; contestant 2 (38)→rank 3; contestant 3 (30)→rank 4; contestant 5 (25)→rank 5.

Step 2 — Rank Judge B's scores. Scores $40,35,32,44,20$, sorted: $44>40>35>32>20$. Contestant 4 (44)→rank 1; contestant 1 (40)→rank 2; contestant 2 (35)→rank 3; contestant 3 (32)→rank 4; contestant 5 (20)→rank 5.

Step 3 — Tabulate both rank columns and find $d, d^2$.

$\sum d^2=2$ (no tied ranks, so the standard formula applies directly).

Step 4 — Apply the formula, $n=5$.

Independent check. Three of the five contestants (2, 3, 5) received the identical rank from both judges ($d=0$), and the other two (1 and 4) merely swapped ranks 1 and 2 — a very small, consistent disagreement, matching a high $r_s$ of $0.9$ rather than a moderate or weak value.

Ranking a judge's scores from lowest to highest instead of highest to lowest (or being inconsistent between the two judges) inverts the calculation — always fix a single convention and apply it identically to both judges.