We use our Roth IRA as an emergency fund of sorts, but it's not our short-term emergency fund. We have about $10K in a regular savings account earning almost nothing, but that's our go-to emergency fund. When a huge branch broke the living room window, for example, we paid for it out of that. We have incredibly secure jobs with very little chance of a layoff, so that $10K does not represent 3 months' of living expenses, but it's enough to deal with expensive, unexpected blows.
If something really horrendous were to happen (catastrophic injury to one of us, natural disaster requiring relocation, long-term illness, etc.) then I know we would be able to dip into our Roth money. We've never had to do that, though, and hopefully we will never have to. We'd rather grow our $10K savings to $20K simply to prevent having to take money out of investments.
All of this is a preface to saying no, I don't think it's a good idea to put $4k of your $5K into your Roth IRA. It's not liquid enough, and many emergencies cost more than $1K. Low returns are a bummer, but having to sell investments at a bad time and giving up future returns on that money is worse. Plus, you only mention higher returns, but losing money is also a very real possibility. What if something terrible happens, you need $3,500, and it turns out that the market's been doing poorly, and your $5K is only worth about $4K at that time? Emergencies are stressful enough on their own, but it will be downright painful feeling forced to sell at that moment, and that will just add to the stress.
If you still want to maximize your returns, I'd keep the $5K liquid, put it out of your mind, and then start siphoning more money into your Roth on a monthly basis.