My stock '98 F-150 4.6L V-8 4WD Automatic with 3.5:1 rear end and 112,000 miles is maxed out towing my 5,000 lb travel trailer. Is it reasonable to expect that a cold air intake and after market muffler would measurably improve power and gas mileage? Are there downsides to such modifications? I am also considering moving up to an '01 or '02 F-150 with the 5.4 L V-8. Comments appreciated?
The cheapest solution to your problem is to get a truck with a more powerful engine. There isn’t really anything you can do with this one that is affordable to make it a more capable tow rig, unless you want to try numerically higher axle gears. An aftermarket muffler and intake system will make the truck louder but not provide any significant increase in performance. You may also look at some other makes that can meet your expectations. I used to have an F-150 with a 4.6L engine that seemed plenty powerful, although I never towed with it. On the other hand, I’ve had a few Chevy trucks with a 350, both carbureted and fuel injected, and have towed trailers weighing 6,000 pounds or more, and they performed very well, even my four barrel carb '86 with 2.73:1 gears. I also had a 3/4 ton Chevy with a fuel injected 350 that hardly seemed to notice a 7,000 pound race car trailer it towed on a fairly regular basis.
Doing those 2 mods to your truck won’t really help. May look cool to you, may sound cool, but performance wise, on that vehicle, you won’t see much difference. If you’re after noise and looks, go for it. If not, you’re best move (as Mark said), is a different truck. 
I would just trade up to a 5.4 powered truck…The 4.6, 280 cubic inches, just doesn’t have the torque to pull a trailer comfortably…
And if you decide to trade, do it soon, just to make sure your tranny doesn’t croak during ‘one last tow’.
You say that your truck is maxed out at 5000 lbs. Is that only doe to horsepower? Are the trucks suspension, cooling system, transmission and brakes made to handle a heavier load? If not, you will not only need a lot more HP, but a number of other expensive upgrades.
To significantly increase your HP, you could add an aftermarket supercharger. They are available for this engine for around $1200 I think, but then you will need premium fuel all the time and there are the other considerations.
FWIW, I looked up your truck a Edmunds.com. They say it can tow 7500#.
Those 2 modifications won’t accomplish anything and a 4WD F150 lugging an additional 2.5 tons is asking an awful lot of a small displacement motor; especially one with a near square motor as to bore and stroke.
You would be better off finding a substitute; either a more powerful gas engine or a diesel rig.
It will do it, but you have to lock out the overdrive and flog the engine, keeping the RPM’s uncomfortably high…
The mods you suggest are really only effective at high RPMs, not for towing at a steady low to mid-range RPM. I’m with the people that say get a different truck. If you do a lot of towing, a diesel will be the best compromise for power and mileage.
The old 4.9L engine was more suitable to such demands. The square 4x4 cylinders and tractor like cam grind made for a great deal of power at relatively low RPMs. I cannot understand why Ford scrapped that engine. Like the GM 292, the Ford 300 (4.9L) was a master piece of simple, stump pulling power.
Regardless what it was rated for in 98, it’s 13 years old and 5k isn’t unreasonable. I agree, get something newer and bigger if you safely want to tow more.
From the TV commercials it would appear that any pickup could easily tow the U.S.S. Nimitz with no problems. 
Yup. And a Volvo can drive up a ski jump. No problem. You have to love them commercials!
Is THAT why pickups are shown pulling a load of 4’ culvert pipe? All air, but looks HEAVY.