If you didn't move in together until May, you can both file HoH for 2018 as you both (probably) paid more than half the total yearly household expenses*, for your respective dependents, for 2018.
However, going forward (2019+), only one of you can claim HoH. The other will have to file single. Getting married by 12-31-19 would allow you to file as Married Filing Jointly (MFJ).
*100% for 5 months + 50%(+/-) for 7 months = more than half of the year's total.
