LED strip power supply requirements
If some steps aren't taken, then your imagination is right. The input current has to at least equal the output current. However, there are lots of ways to take some extra steps.

For example, you can use a transformer where its primary is designed for the AC mains voltage and where it produces an output voltage much closer to the desired voltage. A transformer will dissipate a small amount of parasitic power (it will leach some power in order to do its job), but it is reasonably efficient and can yield a lower-voltage, higher-current arrangement that changes what you imagined is required. You might use a \$6.3\:\textrm{V}_\textrm{AC}\$ secondary power transformer, for example, in order to get a voltage that is closer to the desired \$5\:\textrm{V}\$ and then add some circuitry to finish the job. If you use this method, then the current load on the AC mains supply will be quite a bit less than the current required by your LED strip.

Or, you might use what's called a "switcher," where it is designed to operate directly from the AC mains supply. These will use inductors and capacitors in a somewhat more complex arrangement than the above-mentioned transformer method and they will usually be smaller and weigh less and probably be cheaper, too (as AC mains transformers tend to be heavy and expensive, by comparison.) These also can be very efficient in terms of transforming power.

A transformer-based method starts out with reasonable efficiency with the transformer itself, but often needs some significant control "overhead" voltage and for \$5\:\textrm{V}\$ systems this might mean you get efficiencies that are perhaps as good as 60%. Switchers can usually achieve better, at the expense of some complexity but lower costs because of avoiding an expensive and heavy transformer. Perhaps 75-80% for an efficiency figure, but just be aware that this value can vary widely depending upon the specific design and how it relates to your specific needs.

You can boil all this down to a simple efficiency figure, such as 75% or 80% (or 60%, let's say, for the transformer method), and a power consideration. In your case, you need \$90\:\textrm{W}\$ of delivered power. Just divide the efficiency figure into your power requirement to figure out the AC mains power. Divide that by the AC mains RMS voltage and you get the required current.

Let's say the efficiency is 70%. Then the power required from the AC mains will be about \$\frac{90\:\textrm{W}}{70\%}\approx 130\:\textrm{W}\$. If the AC mains voltage is \$120\:\textrm{V}_\textrm{RMS}\$ then the current will be \$\approx 1.1\:\textrm{A}_\textrm{RMS}\$. If the AC mains voltage is \$220\:\textrm{V}_\textrm{RMS}\$ then the current will be \$\approx 0.6\:\textrm{A}_\textrm{RMS}\$.

So you can see that this is a lot smaller than you were otherwise expecting.

As others have already mentioned, you probably don't need a high precision \$5\:\textrm{V}\$ supply. But you probably do need a power supply that can hold \$5\pm 0.2\:\textrm{V}\$ at the current rating into the load that you need, which is about \$20\:\textrm{A}\$. So it would be a good idea to make sure that the power supply is rated for at least that much (more is usually better) current and that it is rated to hold the voltage within a reasonable margin around your specified voltage over variations of the AC mains supply voltage and over some range of your load's current requirements, too. This starts to get more technical, now.

A thorough design would take into account various risks, including risks of fire. An LED strip that is dissipating \$90\:\textrm{W}\$ over \$5\:\textrm{m}\$ length isn't likely, by itself, to start a fire. But a power supply that is connected to the mains and which may be, itself, dissipating \$40-50\:\textrm{W}\$ into a small volume buried inside a wall might actually cause a fire. So please also consider other aspects of your work. The power supply itself needs to have some safety measures built into its design and it needs to be arranged in a location where its dissipation can be reasonably accommodated. We often just assume you'd do that. But I've seen cases where people have placed SSRs with \$100\:\textrm{W}\$ of dissipating heat sinks attached and just buried them into their thin walls as though that was a safe thing to do. So be careful.