In a typical lottery, the primary function at action is statistical mechanics. By comparison, in most sports gambling scenarios one is betting against the pool of other betters and it is this pool that determines the odds. This is known as Parimutuel betting and can be compared with fixed-odds betting arrangements in which one is gambling against the house, which is setting the odds and payoff usually at the time of the bet, and those odds can shift through time until betting window closes as the house tries to spread out their risk to not only cover betting, but to make a profit.

I'm not sure which sportsbook you're quoting for the 5000-1 odds, but I would suppose that it is parimutuel and the house "sets" the game and takes a percentage off of the top (known as the rake or vigorish) as does the local government in taxes. The odds are then determined by the number of betters and the teams for which they're betting. If the pool of betters (presumably all having the same information) is "right", then the odds set are typically "correct" and the proper/fair payouts follow.

In cases where the betting pool is overly biased (perhaps there are more die hard fans for Man United who are betting with their hearts and not their brains) this can create situations known as "overlays" in which careful gamblers who notice the shift can take advantage of the situation and potentially have better-than-usual margins on their bets. Naturally these margins need to be big enough to overcome not only the inherent risk of the initial gamble, but also cover the loss of the houses's rake and the subsequent taxes. Serious handicappers will use all of the best available information available in making their gambling choices, but will then only proceed to place bets on which they perceive to be overlays. In the long run this will give them a slight edge (not over the house, but) over their fellow gamblers. They also typically place their bets just before the close of betting so that they have the most updated odds available (and can ensure their bet is still an overlay) while keeping in mind that their bet and other last-minute bets can potentially sway the ultimate odds. (example: If someone comes in at the last minute with several million pounds on Leicester City then the odds shift away from them, potentially creating overlays for other teams.)

In most cases, longshots with terrible odds like these, are longshots for a reason, but if a careful gambler has (preferably solid information creating) reason to believe that the odds shouldn't be as bad as they are, then it creates an overlay which makes the bet more valuable in comparison to all the other gamblers.

For statisticians, think of it as a normal curve whose local x-value along the y-axis is shifting (usually slightly) over time. If there's a huge bump in the outlying choices just before betting closes, then one's statistical likelihood of winning is better and it's a good bet with a better-than-average payoff. In practice, there are so many people gambling (usually intelligently) that these local shifts (sometimes called "noise" in engineering parlance) are fairly small and that in aggregate averaged over time most gambling situations are the mathematical equivalent of a numerical lottery.

As a similar somewhat related example, in US baseball, sabermetricians are gathering large amounts of data to attempt to find otherwise unseen inequities in forecasted player talent and then leverage that to try to win more baseball games. In the early days of applying these methods, one team could statistically do better than others, however over time, as more teams begin using the same methods, the information gap is overcome and everyone is on equal footing again. The trouble in most sports is that coming up with accurate measurements of performance isn't easy (or even statistically significant) and thereby adds a large enough layer of noise on top of the process that gambling on them is again relatively equivalent to the lottery.