$5 is a fraction, fully expanded we should write it as BTC / $
So with a greater Dollar price we should then expect a lower BTC price as a result. If the Dollar currency should double in value and purchasing power then we have to expect by default that the BTC price is halved.
The reason to suspect that BTC price will not be falling long term in full consideration is that Dollar is not likely to double in value or even retain the value it had in 2019. The value of US dollar is falling in line with the fiscal deficit spending that is occurring and this is similar to many countries now which will deliberately overspend. Its a political policy to degrade the value of the national currency and place that value in overspending, doesn't matter our views on it as we just have to decide if its a reality and likely to continue. If dollar is to continually lose value then lower prices for many things in use globally are unlikely, this is our backdrop for considering such a negative view as $5 BTC price.
So long as BTC is valid value exchange and stable in its known monetary base then great loss of value is unlikely until there is a far better alternative then most choices available now. Price doesnt have to go up but I only think a failure is going to be especially harsh on its outcome over years, at least in dollar value.