5000 Watts ÷ 48 Volts = 104 Amps Draw.
Low Frequency Inverter can do 3X Surge while a High Frequency can only do 2X Surge.
The general rule of thumb is to not exceed 250A Draw from a battery bank. Other things come into play after that level.
So assuming 250A Max @ 48V = 12,000W or 120V/100A or 240V @ 50A.
** These are GROSS Numbers not corrected for inversion losses. HF vs LF Inverters have different efficiencies. Tier-1 Products like Victron, Samlex tend to be around 94% Efficient while lower-level products can drop to 82% efficiency. In General Growatt is Mid to High 80% Efficient, some of their higher end models are better.
ALSO BE AWARE of the Standby / Idle energy consumption ! THAT can be Very Significant !
I run a single bank of 5 large packs for 1190AH/30.4kWh. I am converting this to a Split Bank which will have 2x 175AH on one leg and 3x 280AH on the other leg of the bank using a dual common DC BUS. Once you go past 4 Packs in one bank, things get strange!
I use pairs of these Covered Busbars which are rated for 250A and the best deal I could find on them ATM is from here which just supplied me with a final pile of gear,
https://www.ebay.ca/itm/152438375154 They delivered Fast & OnTime !
Fuses: I am a tad unusual as I use MRBF Fuses as opposed to Class-T Fuses (kept wrecking those). They are on average about $30 USD ea with the Terminal Block. I use ONLY BlueSea ones which are made by Eaton/Bussman and are Top Quality. All of mine are 250A.
BlueSea Link:
https://www.bluesea.com/products/5191/MRBF_Terminal_Fuse_Block_-_30_to_300A
KNOW your Battery Pack !
Using my example, I use 280AH Packs.
They are physically capable of outputting up to 280A for 1 hour and take 140A for 2 hours to charge. They are Burst Discharge Capable up to 5C for 60 Seconds (varies by maker a bit). Therefore you need to fuse them to the max you will allow, 250A is quite enough. ALSO if you add battery packs in Parallel, any Load of Charge will be divided
proportionately between the packs. This is IMPORTANT TO NOTE. This si one of the reasons to keep battery packs within a battery bank close to each others capacities as it is very easy to introduce an unbalancing factor if the difference is too much.
A last thought to ponder.
Typically if building a Bank of 2 or more packs, it is best to configure them to be capable of working (charge & discharge) as a "Stand Alone" or "Last Man Standing", This allows for Fail Over Fault Tolerance should any pack decide to cutoff for any reason. This means that whatever BMS you select should be capable of handling your maximums for Charge & Discharge.
A WARNING !
As stated I have a fairly large bank plus I have utility packs as well, all LFP. This has all been put together over the past couple of years as I moved away from the Heavy Lead Acid. The gotcha was different versions of BMS and a slight mix of gear resulting from the evolution. I am now replacing about $2500 USD worth of BMS, Contactors & more to Normalize & Simplify all the packs to have identical BMS and Communications / interactive capabilities. Let alone the cost of all the new BMS' and related goodies on top... So really do PLAN THINGS AHEAD !
Hope it helps, Good Luck