The late-season run makes it a lot harder to evaluate Arsenal's season. 5th place is their worst finish under Wenger, but they finished with 75 points and a +33 GD, which is not really any better or worse than they've been in any of the last ten years, and four points better than their 2nd-place finish last year. The difference this year was that 1) the quality of the rest of the top 6 jumped enormously, and 2) their underlying performance metrics (e.g. xGD) declined significantly. They were not nearly as good this year, and only a superhuman season from Sanchez (24G, 10A) covered up a lot of the decline. If Sanchez leaves they could be really screwed -- where are the goals going to come from?
As MMS points out, Arsenal's big problem is that this team was built to peak the last two years, but didn't get over the hump, and it doesn't look like they have a plan for what to do next. The original plan, I think, was that the once-young, now-prime-age British talent (Walcott, Ramsey, Ox, Wilshere, Gibbs, etc.) was going to develop and carry the team forward, but none of those guys panned out as anything more than useful squad players for a side that wants to compete for titles. Arsene's biggest failure the last several years was probably to not cut bait with that development plan sooner and sell those players at the peak of their value. Part of the tolerance for not competing for the title in the 2009-13 period was that the club was building something for the future. That is no longer the case.
Arsenal can't afford to compete on transfers with Man U/City/Chelsea, which means to build a team they need to find budget diamonds and/or develop internally. And the internal development pipeline has dried up. The knock-on effect of their weaker development program has been very little in incoming transfer revenue. Wenger has failed to turn over the bottom half of his squad to generate revenue that could be used to buy more promising players. Arsenal's combined income from player sales the last two seasons is only 11m; the last four seasons combined is only 45m. For comparison, Spurs' transfer revenue the last two years is 119m and the last four years is 272m. The four-year number is boosted by the Bale transfer, but Spurs have also sold a bunch of mediocre players who aren't good enough to play for them for real money (they got 51m combined for Ryan Mason, Nacer Chadli, Andros Townsend, and Paulinho). Liverpool have done something similar, getting 28m last year for spare parts Jordan Ibe and Joe Allen, which allowed them to buy a guy like Wijnaldum who fits their team much better.
If Arsenal can hold onto Sanchez, Ozil, and Bellerin AND sign 2-3 more legit starters (which will require a net spend of >60m), they could compete for the title next year with some breaks, but they would probably be something like joint 4th favorites heading into the season even under that best-case scenario. If they lose Sanchez and Ozil and don't buy superstars to replace them, they will probably struggle to compete for a CL spot.
A year ago I thought Wenger-out was silly, because they probably had the best team in 2015-16 and the team appeared to be peaking, and it was worth giving Wenger one more shot at the title. Last summer, I picked them to win the title this season. But I think this season made clear that Wenger has missed his chance and is getting left behind by the more progressive clubs. He's never fully figured out how to cope with the new hyper-aggressive pressing tactics that Spurs, Liverpool, and City use. The lack of any discernible long-term strategic plan is the reason I think Arsenal should be moving on from Wenger.
